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Call number: | 9781470416379::ONLINE Show nearby items on shelf |
Title: | Glimpses of soliton theory: The algebra and geometry of nonlinear PDEs |
Author(s): |
Alex Kasman |
Date: | 2010 |
Publisher: | Providence, R.I.: American Mathematical Society |
Size: | 1 online resource (304 pages) |
Note: | Limited User Access (3 Copies Available) |
Contents: | Differential equations, Developing PDE intuition, The story of solitons, Elliptic curves and KdV traveling waves, KdV -solitons, Multiplying and factoring differential operators Eigenfunctions and isospectrality, Lax form for KdV and other soliton equations, The KP equation and bilinear KP equation, The Grassmann cone Γ_{2,4} and the bilinear KP equation Pseudo-differential operators and the KP hierarchy, The Grassman cone and the bilinear KP hierarchy, Concluding remarks, Mathematica guide, Complex numbers, Ideas for independent projects |
ISBN: | 9781470416379 |
Series: | Student mathematical library, v. 54. |
Series: | eBooks |
Series: | EBSCOhost |
Keywords: | Korteweg-de Vries equation. , Geometry, Algebraic. , Differential equations, Partial. |
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Call number: | SPRINGER-2016-9783319206905:ONLINE Show nearby items on shelf |
Title: | New Approaches to Nonlinear Waves |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (15 p.) |
Note: | 10.1007/978-3-319-20690-5 |
Contents: | Introduction (E. Tobisch) -- Brief historical overview -- Main notions -- Resonant interactions -- Modulation instability -- Frameworks -- Reality check -- References -- The effective equation method (Sergei Kuksin and Alberto |
Maiocchi) -- Introduction -- How to construct the effective equation -- Structure of resonances -- CHM: resonance clustering -- Concluding remarks -- References -- On the discovery of the steady-state resonant water waves (Shijun Liao, | |
Dali Xu and Zeng Liu) -- Introduction -- Basic ideas of homotopy analysis method -- Steady-state resonant waves in constant-depth water -- Experimental observation -- Concluding remarks -- References -- Modulational instability in | |
equations of KdV type (Jared C. Bronski, Vera Mikyoung Hur and Mathew A. Johnson) -- Introduction -- Periodic traveling waves of generalized KdV equations -- Formal asymptotics and Whitham’s modulation theory -- Rigorous theory of | |
modulational instability -- Applications -- Concluding remarks -- References -- Modulational instability and rogue waves in shallow water models (R. Grimshaw, K. W. Chow and H. N. Chan) -- Introduction -- Korteweg-de Vries equations -- | |
Boussinesq model -- Hirota-Satsuma model -- Discussion -- References -- Hamiltonian framework for short optical pulses (Shalva Amiranashvili) -- Introduction -- Poisson brackets -- Pulses in optical fibers -- Hamiltonian description of | |
pulses -- Concluding remarks -- References -- Modeling water waves beyond perturbations (Didier Clamond and Denys Dutykh) -- Introduction -- Preliminaries -- Variational formulations -- Examples -- Discussion -- References -- | |
Quantitative Analysis of Nonlinear Water-Waves: a Perspective of an Experimentalist (Lev Shemer) -- Introduction -- The experimental facilities -- The Nonlinear Schrödinger Equation -- The Modified Nonlinear Schrödinger (Dysthe) | |
Equation -- The Spatial Zakharov Equation -- Statistics of nonlinear unidirectional water waves -- Discussion and Conclusions -- References | |
ISBN: | 9783319206905 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Physics: 908 |
Keywords: | Physics , Continuum physics , Geophysics , Statistical physics , Dynamical systems , Physics , Theoretical, Mathematical and Computational Physics , Classical Continuum Physics , Statistical Physics, Dynamical Systems and Complexity , Geophysics and Environmental Physics |
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Call number: | SPRINGER-2014-9783034807364:ONLINE Show nearby items on shelf |
Title: | Dispersive Equations and Nonlinear Waves [electronic resource] : Generalized Kortewegde Vries, Nonlinear Schrdinger, Wave and Schrdinger Maps |
Author(s): |
Herbert Koch Daniel Tataru Monica Vian |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalizedKorteweg-de Vries equatio n and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrdinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concreteexample, it walks the reader through the inductio n on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almostperiodicity of minimal blow up solutions, and the development of long- time Strichartz inequalities. The third part describes wave and Schrdinger maps. Starting by building heuristics about multilinear estimates, it provides adetailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and id eas and should provide graduate students with a stepping stone to this exciting direction of research |
ISBN: | 9783034807364 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Oberwolfach Seminars, 1661-237X : v45 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2012-9780817682651:ONLINE Show nearby items on shelf |
Title: | Nonlinear Partial Differential Equations for Scientists and Engineers [electronic resource] |
Author(s): |
Lokenath Debnath |
Date: | 2012 |
Edition: | Third Edition |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | An exceptionally complete overview of the latest developments in the field of PDEs. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something foreveryone here. Applied Mec hanics Review (Review of First Edition) Overall, it is a useful book for teaching, a rich source of examples, and I am happy to have it on a shelf of my library. UK Nonlinear News (Review of SecondEdition) The revised and enlarged third edition of this su ccessful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their various current applications. In an effort tomake the book more useful for a diverse readership, updated modern examples of ap plicationshave beenchosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics,acoustics, and wave propagation. The book gives thorough coverage of the derivation and solution methods for all fundamental nonlinear model equations, such as Kortewegde Vries, CamassaHolm, DegasperisProcesi,EulerPoincar, Toda lattice, Boussinesq, Burgers, Fisher, Whitham, nonlinear KleinGordon, sine-Gordon, nonlinear Schrdinger, nonlinear reaction-diffusion, and E ulerLagrange equations. Other topics and key featuresinclude: * Improved presentations of results, solution methods, and proofs. * Solitons, gravity-capillary solitary waves, and the Inverse Scattering Transform. * Special emphasis on compactons, intrinsi c localized modes, andnonlinear instability of dispersive waves with applications to water waves and wave breaking phenomena. * New section on the Lorenz nonlinear system, the Lorenz attractor, and deterministic chaos, and new examples of nonlinearquasi-h armonic waves, modulational instability, nonlinear lattices, and the Toda lattice equation. * Over 1000 worked-out examples and end-of-chapter exercises with expa |
Note: | Springer eBooks |
Contents: | Preface to the Third Edition |
Preface | |
Linear Partial Differential Equations | |
Nonlinear Model Equations and Variational Principles | |
First | |
Order, Quasi | |
Linear Equations and Method of Characteristics | |
First | |
Order Nonlinear Equations and Their Applications | |
Conservation Laws and Shock Waves | |
Kinematic Waves and Real | |
World Nonlinear Problems | |
Nonlinear Dispersive Waves and Whitham's Equations | |
Nonlinear Diffusion | |
Reaction Phenomena | |
Solitons and the Inverse Scattering Transform | |
The Nonlinear Schroedinger Equation and Solitary Waves | |
Nonlinear Klein | |
Gordon and Sine | |
Gordon | |
ISBN: | 9780817682651 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2008-9781402084911:ONLINE Show nearby items on shelf |
Title: | The Painlev Handbook [electronic resource] |
Author(s): |
Robert Conte Micheline Musette |
Date: | 2008 |
Publisher: | Dordrecht : Springer Netherlands |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems),and biology (competit ion of species). This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, andthis can be achieved without any a priori kno wledge of the solutions, with a powerful algorithm presented in detail called the Painlev test. If the equation under study passes the Painlev test, the equation is presumed integrable.If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions. The examples chosen to illustrate these methods are mostly taken from physics. These include on theintegrable side the nonlinear Schrdinger equation (continuous and discrete), the Korteweg-de Vries equation, the Hnon-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in opticalfibers, turbulence, etc), the Kuramoto-Sivashinsky equation (phase turbulence), the Kolmogorov-Petrovski-Piskunov equation (KPP, a reaction-diffusion model), the Lorenz model of atmospheric circulation and the Bianchi IX cosmologicalmodel. Written at a graduate level, the book contains tutorial text as well as detailed examples and the state of the art on some current research |
Note: | Springer eBooks |
ISBN: | 9781402084911 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry Mathematics , Differentiable dynamical systems , Differential Equations , Differential equations, partial , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2005-9780817644185:ONLINE Show nearby items on shelf |
Title: | Nonlinear Partial Differential Equations for Scientists and Engineers [electronic resource] |
Author(s): |
Lokenath Debnath |
Date: | 2005 |
Edition: | Second Edition |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is avery hard act to follow, a nd recommends it strongly. [This book] is a jewel. ---Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear andnonlinear partial differential equations and their v aried applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics,plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for adiverse readership. Topics and key features: * Thorough coverage of derivation and methods of sol utions for all fundamental nonlinear model equations, which include Korteweg--de Vries, Boussinesq, Burgers, Fisher, nonlinearreaction-diffusion, Euler--Lagrange, nonlinear Klein--Gordon, sine-Gordon, nonlinear Schrdinger, Euler, Water Waves, Camassa and Holm, Johnson, Davey-Stewartson, Kolmogorov, Petrovsky and Piscunov, Kadomtsev and Petviashivilli,Benjamin, Bona and Mahony, Harry Dym, Lax, and Whitman equations * Systematic presentation and explanation of conservation laws, weak solutions, and shock wa ves * Solitons, compactons, intrinsic localized modes, and the InverseScattering Transform * Special emphasis on nonlinear instability of dispersive waves with applications to water waves * Over 600 worked examples and end-of-chapter exercises with hints and selected solutions New features of the SecondEdition include: * Improved presentation of results, methods of solutions, and proofs * New section on Sturm--Liouville systems and their fundamental |
Note: | Springer eBooks |
Contents: | Linear Partial Differential Equations |
Nonlinear Model Equations and Variational Principles | |
First | |
Order, Quasi | |
Linear Equations and Method of Characteristics | |
First | |
Order Nonlinear Equations and Their Applications | |
Conservation Laws and Shock Waves | |
Kinematic Waves and Real | |
World Nonlinear Problems | |
Nonlinear Dispersive Waves and Whithams Equations | |
Nonlinear Diffusion | |
Reaction Phenomena | |
Solitons and the Inverse Scattering Transform | |
The Nonlinear Schrdinger Equation and Solitary Waves | |
Nonlinear Klein | |
Gordon and Sine | |
Gordon Equations | |
Asymptotic Methods and Nonlin | |
ISBN: | 9780817644185 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Mathematical physics , Engineering mathematics |
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Location: | ONLINE |
Call number: | SPRINGER-2001-9783540452768:ONLINE Show nearby items on shelf |
Title: | Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory |
Author(s): |
Peter E Zhidkov |
Date: | 2001 |
Size: | 1 online resource (154 p.) |
Note: | 10.1007/3-540-45276-1 |
Contents: | Introduction -- Notation -- Evolutionary equations. Results on existance: The (generalized Korteweg-de Vries equation (KdVE) The nonlinear Schrödinger equation (NLSE) On the blowing up of solutions Additional remarks -- Stationary |
problems: Existence of solutions. An ODE approach Existence of solutions. A variational method The concentration-compactness method of P.L. Lions On basis properties of systems of solutions Additional remarks -- Stability of solutions: | |
Stability of soliton-like solutions Stability of kinks for the KdVE Stability of solutions of the NLSE nonvanishing as (x) to infinity Additional remarks -- Invariant measures: On Gaussian measures in Hilbert spaces An invariant | |
measure for the NLSE An infinite series of invariant measures for the KdVE Additional remarks -- Bibliography -- Index | |
ISBN: | 9783540452768 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1756 |
Keywords: | Mathematics , Partial differential equations , Physics , Mathematics , Partial Differential Equations , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-1998-9783034888103:ONLINE Show nearby items on shelf |
Title: | Scaling Limits and Models in Physical Processes |
Author(s): |
Carlo Cercignani |
Date: | 1998 |
Size: | 1 online resource (194 p.) |
Note: | 10.1007/978-3-0348-8810-3 |
Contents: | I Scaling and Mathematical Models in Kinetic Theory -- 1 Boltzmann Equation and Gas Surface Interaction -- 2 Perturbation Methods for the Boltzmann Equation -- II Scaling, Mathematical Modelling, & Integrable Systems -- 1 Dispersion |
-- 2 Nonlinear Schrödinger Equation -- 3 Korteweg-de Vries -- 4 Isospectral Deformations -- 5 Inverse Scattering Theory -- 6 Variational Methods -- 7 Weak and Strong Nonlinearities -- 8 Numerical Methods | |
ISBN: | 9783034888103 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | DMV Seminar : 28 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematical physics , Physics , Mathematics , Analysis , Mathematical Physics , Physics, general |
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Call number: | SPRINGER-1996-9783034875189:ONLINE Show nearby items on shelf |
Title: | Nonlinear Dynamical Systems and Chaos |
Author(s): | |
Date: | 1996 |
Size: | 1 online resource (463 p.) |
Note: | 10.1007/978-3-0348-7518-9 |
Contents: | Symmetries in dynamical systems -- Symplccticity, reversibility and elliptic operators -- The Rolling Disc -- Testing for Sn-Symmetry with a Recursive Detective -- Normal forms of vector fields satisfying certain geometric conditions |
-- On symmetric ?-limit sets in reversible flows -- Symmetry Breaking in Dynamical Systems -- Invariant Cj functions and center manifold reduction -- Hopf bifurcation at k-fold resonances in conservative systems -- KAM theory and other | |
perturbation theories -- Families of Quasi-Periodic Motions in Dynamical Systems Depending on Parameters -- Towards a Global Theory of Singularly Perturbed Dynamical Systems -- Equivariant Perturbations of the Euler Top -- On stability | |
loss delay for a periodic trajectory -- Parametric and autoparametric resonance -- Global attractors and bifurcations -- Infinite dimensional systems -- Modulated waves in a perturbed Korteweg-de Vries equation -- Hamiltonian | |
Perturbation Theory for Concentrated Structures in Inhomogeneous Media -- On instability of minimal foliations for a variational problem on T2 -- Local and Global Existence of Multiple Waves Near Formal Approximations -- Time series | |
analysis -- Estimation of dimension and order of time series -- Numerical continuation and bifurcation analysis -- On the computation of normally hyperbolic invariant manifolds -- The Computation of Unstable Manifolds Using Subdivision | |
and Continuation | |
ISBN: | 9783034875189 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Nonlinear Differential Equations and Their Applications : 19 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Numerical analysis , Manifolds (Mathematics) , Complex manifolds , Mathematics , Analysis , Manifolds and Cell Complexes (incl. Diff.Topology) , Numerical Analysis |
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Call number: | SPRINGER-1995-9781461384601:ONLINE Show nearby items on shelf |
Title: | Control and Optimal Design of Distributed Parameter Systems |
Author(s): | |
Date: | 1995 |
Size: | 1 online resource (246 p.) |
Note: | 10.1007/978-1-4613-8460-1 |
Contents: | A shape optimization problem in inverse acoustics -- On a variational equation for thin shells -- Oriented distance functions in shape analysis and optimization -- On the density of the range of the semigroup for semilinear heat |
equations -- Relaxation in semilinear infinite dimensional systems modeling fluid flow control problems -- Multidimensional inverse scattering problems in deterministic and random media -- Decay estimates for the wave equation -- | |
Asymptotic behavior and attractors for nonlinear Von Kármán plate equations with boundary dissipation -- Stabilization of the Korteweg-De Vries equation on a periodic domain -- A note concerning boundary effects and long time | |
vibrations of layered media -- On the linearised dynamics of linked mechanical structures | |
ISBN: | 9781461384601 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | The IMA Volumes in Mathematics and its Applications: 70 |
Keywords: | Mathematics , System theory , Calculus of variations , Mathematics , Systems Theory, Control , Calculus of Variations and Optimal Control Optimization |
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Call number: | SPRINGER-1994-9783034885300:ONLINE Show nearby items on shelf |
Title: | Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena International Conference in Vorau (Austria), July 18–24, 1993 |
Author(s): | |
Date: | 1994 |
Size: | 1 online resource (402 p.) |
Note: | 10.1007/978-3-0348-8530-0 |
Contents: | A semigroup formulation of a nonlinear size-structured distributed rate population model -- Damage detection and characterization in smart material structures -- Optimality conditions for non-qualified parabolic control problems -- |
Convergence of trajectories for a controlled viscous Burgers’ equation -- Optimality conditions for boundary control problems of parabolic type -- Pontryagin’s principle for optimal control problems governed by semilinear elliptic | |
equations -- Invariance of the Hamiltonian in control problems for semilinear parabolic distributed parameter systems -- Rate distribution modeling for structured heterogeneous populations -- A model for a two-layered plate with | |
interfacial slip -- Numerical solution of a constrained control problem for a phase field model -- Uniform stabilizability of nonlinearly coupled Kirchhoff plate equations -- Boundary temperature control for thermally coupled | |
Navier-Stokes equations -- Adaptive estimation of nonlinear distributed parameter systems -- Decay estimates for the wave equation with internal damping -- On the controllability of the rotation of a flexible arm -- Modeling and | |
controllability of interconnected elastic membranes -- On feedback controls for dynamic networks of strings and beams and their numerical simulation -- Various relaxations in optimal control of distributed parameter systems -- | |
Convergence of an SQP—method for a class of nonlinear parabolic boundary control problems -- Conditional stability in determination of densities of heat sources in a bounded domain -- Boundary stabilization of the Korteweg-de Vries | |
equation -- Controllability of the linear system of thermoelasticity: Dirichlet-Neumann boundary conditions | |
ISBN: | 9783034885300 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | ISNM International Series of Numerical Mathematics : 118 |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Computer mathematics , Mathematics , Computational Mathematics and Numerical Analysis , Applications of Mathematics |
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Call number: | SPRINGER-1991-9789400919082:ONLINE Show nearby items on shelf |
Title: | Applied and Industrial Mathematics Venice - 1, 1989 |
Author(s): | |
Date: | 1991 |
Size: | 1 online resource (374 p.) |
Note: | 10.1007/978-94-009-1908-2 |
Contents: | I: Invited Papers -- - C. Cercignani, “Physical Problems and Rigorous Results in Kinetic Theory -- - A. Chorin, “Statistical Mechanics of Vortex Filaments” (abstract) -- - Feng Kang, “The Hamiltonian Way for Computing Hamiltonian |
Dynamics” -- - C. W. Gear (with Fen-Lien Juang), “The Speed of Waveform Methods for ODEs” -- - J. B. Keller, “Diffusively Coupled Dynamical Systems” -- - P. D. Lax, “Deterministic Turbulence” (extended abstract) -- - J. L. Lions, | |
“Exact Controllability for Distributed Systems. Some Trends and Some Problems” -- - V. P. Maslov, “Beginning of Weakly Anisotropic Turbulence” -- - S. K. Mitter, “Markov Random Fields, Stochastic Quantization and Image Analysis” -- - | |
H. Neunzert (with F. Gropengießer and J. Struckmeier),. “Computational Methods for the Boltzmann equation” -- - J. R. Ockendon, “A Class of Moving Boundary Problems Arising in Industry” -- - M. Primicerio, “Systems with Non-Fading | |
Memory Encountered in the Modellization of Industrial Problems” -- - M. Pulvirenti, “A Stochastic Particle System Modelling the Broadwell Equation” -- -A. Quarteroni “(with A. Valli), “Theory and Application of Steklov-Poincare | |
Operators for Boundary-Value Problems” -- - S. Rionero (with B. Straughan), “On the Problem of Natural Convection” -- II: Selected Contributed Papers -- 1. Mathematical Modelling in Fluid Mechanics -- - J. A. Nohel, “Non-Newtonian | |
Phenomena in Shear Flow” -- - O. Pironneau (with C. Bernardi, M. O. Bristeau and M. G. Vallet), “Numerical Analysis for Compressible Viscous Isothermal Stationary Flows” -- - E. G. Virga (with D. Roccato), “Drops of Nematic Liquid | |
Crystal Floating on a Fluid” -- 2. Nonlinear waves -- - S. Venakides, “The Korteweg-de Vries Equation with Small Dispersion: Higher Order Lax-Levermore Theory” -- - P. L. Christiansen, “Solitons in Optical Fibres” -- 3. Wave | |
Propagation in Random Media -- - R. Burridge, “Waves in Finely Layered Media” -- - B. S. White (with Balan Nair), “Stochastic Geometry and the Intensity of Random Waves” -- - V. I. Klyatskin, “Plane Waves in Layered Random Media. The | |
Role of Boundary Conditions” -- 4. Transport Phenomena -- - P. A. Markowich (with A. Arnold), “Quantum Transport Models for Semiconductors” -- - G. C. Pomraning, “Particle Transport in Random Media” -- 5. Inverse Problems in the | |
Applied Sciences -- - G. Alessandrini, “Determining Conductivity by Boundary Measurements, the Stability Issue” -- - G. Caviglia (with A. Morro), “Scattering Problems for Acoustic Waves” -- - W.L. Dunn (with A. M. Yacout and F. | |
O’Foghludha), “The Use of Single-Scatter Models in Medical Radiation Applications” -- 6. Mathematical Modelling of Industrial Problems -- - Li Tatsien (with Tan Yongji, Pen Yuejun and Li Hailong)“Mathematical Methods for the SP | |
Well-Logging” -- - C.D. Hill (with P. Susskind and V. Giambalvo), “Effective Computation of the Symmetric Lens” -- - L. Brusa, “Mathematical Modelling of Structural Industrial Problems: Methodologies and Algorithms” -- Author Index | |
ISBN: | 9789400919082 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 56 |
Keywords: | Mathematics , Numerical analysis , Mathematical analysis , Analysis (Mathematics) , Mathematical models , Applied mathematics , Engineering mathematics , Mathematics , Mathematical Modeling and Industrial Mathematics , Analysis , Appl.Mathematics/Computational Methods of Engineering , Numeric Computing |
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Call number: | SPRINGER-1991-9783642761720:ONLINE Show nearby items on shelf |
Title: | Nonlinear Evolution Equations and Dynamical Systems Needs ’90 |
Author(s): | |
Date: | 1991 |
Size: | 1 online resource (240 p.) |
Note: | 10.1007/978-3-642-76172-0 |
Contents: | I One-Dimensional Integrable Models -- Some Remarks on the Hirota Bilinear Identity -- Hirota Equations of Level > 1 -- Integrable N ? 0 Component Nonlinear Schrödinger Model, Phase Transitions and Supersymmetry -- A Tri-Hamiltonian |
Extension of the Boussinesq Equation and Its Modification -- A Direct Algebraic Method for Solving Nonlinear Integrable Models -- Multivalued Solitons for a Hybrid Type of the Modified WKI Equation and Related Problems -- Miura Maps at | |
the Turn of a Handle -- On the Integration of the Infinite Toda Lattice -- II Multi-Dimensional (Nonlinear) Models -- Recent Developments in Multidimensional Inverse Scattering -- Asymptotic Bifurcation of Multidimensional Solitons -- | |
Localized Waves in N+1 Dimensions -- Recent Development for Integrable Integro-Differential Equations -- Exactly Solvable Nonlinear Evolution Equations Expressed by Trilinear Form -- A Derivation of Conserved Quantities and Symmetries | |
for the Multi-Dimensional Soliton Equations -- Dromion Solutions for Generic NLS- and KdV-Type Equations -- “Nonstandard” Classes of Integrable Equations in 1+1 and 2+1 Dimensions -- From Polynomial Solutions to a “General” Solution of | |
the BKP Equation -- Solutions of the Davey-Stewartson Equation with Non-Zero Boundary Condition -- Lump Solutions to the BKP Equation -- III Geometric and Algebraic Methods -- Geometry of Ermakov Systems -- Multisoliton Adiabatic | |
Perturbation Theory. Algebraic Approach -- The Algebraic Structure Associated with Systems Possessing Non-Hereditary Recursion Operators -- Homogeneous Manifolds, Factorisation Problems and Modified KdV Equations -- Bäcklund | |
Transformations and Spectral Problems: the Korteweg-de Vries Interacting Soliton Equation and the Action-Angle Transformation -- Integrability of Polynomial-Nonlinear Evolution Equations and Computer Algebra -- Genetic Codes of Lie | |
Algebras and Nonlinear Evolution Equations -- On Some Problems Concerning Local Symplectic Operators -- Infinitesimal Objects of Hypercomplex Systems Generated by Double Adjacent Classes and Nonlinear Differential Equations -- Local | |
Analysis of Nonlinear Equations -- IV Quantum Field Theory -- The q-Deformed Creation and Annihilation Operators as a Realization of the Quantum Superalgebra Bq(0\l) -- The Heisenberg Quantum Group H(l)q: R-Matrix and Non-Commutative | |
Spaces -- Phase Transitions in Kuryshkin’s Algebras -- Semiclassical Quantization of Kowalewski’s Top on 0(4) and 0(3,1) Lie Algebras -- A Model of Electrodynamics in the Momentum Space of Constant Curvature -- V Applications: | |
Nonlinear Optics, Condensed Matter -- Cellular Automaton to Optical Communication: Diversity of Solitons -- Integrable Unstable Model for Interaction of Langmuir Waves with Acoustic Waves in Plasmas -- Self-Localized Excitation in a | |
Polar Medium with Movable Ions -- Nonlinear Waves Dynamics in Nematics Under the Action of Magnetic Fields -- The Action of Effects of Dissipation, Dispersion and Nonstationary Kerr Nonlinearity on the Propagation of Solitons in | |
Resonant Media -- Two-Dimensional Classical Attractors in the Spin Phase Space of the S = 1 Easy-Axis Heisenberg Ferromagnet -- Universal Attractors for Some Dissipative Nonlinear Evolution Equations -- Evolution of Nonlinear Guided | |
Optical Fields in Planar Layered Structures -- Numerical Application of the KP Equation to a Particular Oceanographical Problem -- On a Dimensional Antiferromagnetic Ising Model with Long Range Interaction -- Coherent State Theory and | |
the Field Lattice Model -- Self-Consistent System of Equations for Probability Amplitudes and Displacements in the X-Y Model -- Periodic and Soliton Solutions of the Heat Equation with a Nonlinear Source of Heat -- Stability Properties | |
of Exact Soliton Solutions of the Parametrically Driven, Damped Nonlinear Schrödinger Equation -- Equations for the Frustrated Josephson Junction Array -- List of Participants -- Index of Contributors | |
ISBN: | 9783642761720 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Quantum physics , Quantum computers , Spintronics , Statistical physics , Dynamical systems , Physics , Statistical Physics, Dynamical Systems and Complexity , Quantum Information Technology, Spintronics , Quantum Physics |
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Call number: | SPRINGER-1990-9783642840395:ONLINE Show nearby items on shelf |
Title: | Nonlinear Evolution Equations and Dynamical Systems |
Author(s): | |
Date: | 1990 |
Size: | 1 online resource (233 p.) |
Note: | 10.1007/978-3-642-84039-5 |
Contents: | I Integrable Systems in (2+1)-Dimensions -- Solitons and Dromions, Coherent Structures in a Nonlinear World -- Boundary Value Problems in 1+1 and in 2+1, the Dressing Method, and Cellular Automata -- Exponentially Localized Solitons |
in 2+1 Dimensions -- On the Boundary Conditions of the Davey-Stewartson Equation -- Rational Solutions to the Two-Component K-P Hierarchies -- Construction of Inverse Data in Multidimensions -- II Criteria and Tests of Integrability: | |
Painlevé Property, Hirota Method, Lie-Bäcklund Symmetries -- Examples of Nonclassical Similarity Reductions -- Equations That Pass Hirota’s Three-Soliton Condition and Other Tests of Integrability -- Selection of Solvable Nonlinear | |
Evolution Equations by Systematic Searches for Lie Bäcklund Symmetries -- III Spectral Methods and Related Topics, C-Integrable Systems -- Inverse Problems of Spectral Analysis and the Integration of Nonlinear Equations -- The Inverse | |
Scattering Transform for the Elliptic Sinh-Gordon Equation -- Reflection Coefficients and Poles -- A N × N Zakharov-Shabat System with a Quadratic Spectral Parameter -- On Integration of the Korteweg-de Vries Equation with a | |
Self-consistent Source -- On the Initial Value Problem of the Third Painlevé Equation -- Nonlinear Equations for Soliton Eigenfunctions Are the IST Integrable Equations -- The Geometry and Completeness of the Two-Phase Solutions of the | |
Nonlinear Schrödinger Equations -- N Double Pole Solution and Its Initial Value Problem for the Modified Korteweg-de Vries Equation -- C-Integrable Generalization of a System of Nonlinear PDE’s Describing Nonresonant N-Wave | |
Interactions -- The Burgers Equation: Initial/Boundary Value Problems on the Semiline -- IV Algebraic Approach to Integrability and Hamiltonian Theory -- The Tangent Bundle for Multisolitons: Ideal Structure for Completely Integrable | |
Systems -- Action-Angle Variables and Asymptotic Data -- The Action-Angle Transformation for the Korteweg-de Vries Equation -- Algorithms to Detect Complete Integrability in 1+1 Dimension -- GN Manifolds, Yang-Baxter Equations and ILW | |
Hierarchies -- Integral and Discrete Evolution Equations: A Unified Approach -- An Abstract Tri-Hamiltonian Lax Hierarchy -- On Symplectic and Hamiltonian Differential Operators -- On a Non-Standard Hamiltonian Description of NLEE -- | |
Energy Dependent Spectral Problems: Their Hamiltonian Structures, Miura Maps and Master Symmetries -- Super Hamiltonian Operators and Lie Superalgebras -- Higher (Non-isospectral) Symmetries of the Kadomtsev-Petviashvili Equations and | |
the Virasoro Action on Riemann Surfaces -- A Combinatorial Rule to Hirota’s Bilinear Equations -- Liouville-Arnold Integrability for Scattering Under Cone Potentials -- V Mappings, Cellular Automata and Solitons -- Lattice Equations | |
and Integrable Mappings -- Recent Developments in Soliton Cellular Automata -- Cubic Equation, Newton’s Method and Analytic Functions -- Singularity of Differential Mappings and Stability of Solitons -- VI Physical Applications -- | |
Action-Angle Variables in the Quantum Wess-Zumino-Witten Model -- On the Derivation of Propagator and Bound State Equations and S-Matrix Elements for Composite States -- Resonant Flow over Topography -- Taxonomy of Ocean Stability | |
Conditions -- Kinetic Equations and Soliton Diffusion in Low-Dimensional Magnets -- On Einstein’s Equations with Two Commuting Killing Vectors -- List of Participants -- Index of Contributors | |
ISBN: | 9783642840395 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
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Keywords: | Physics , Quantum physics , Quantum computers , Spintronics , Statistical physics , Dynamical systems , Physics , Statistical Physics, Dynamical Systems and Complexity , Quantum Information Technology, Spintronics , Quantum Physics |
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Call number: | SPRINGER-1990-9783642752988:ONLINE Show nearby items on shelf |
Title: | Inverse Methods in Action Proceedings of the Multicentennials Meeting on Inverse Problems, Montpellier, November 27th – December 1st, 1989 |
Author(s): | |
Date: | 1990 |
Size: | 1 online resource (125 p.) |
Note: | 10.1007/978-3-642-75298-8 |
Contents: | Modelling or Solving Inverse Problems? -- I Tomographic Inverse Problems -- Tomography with Diffusion, -- Medical Imaging: State-of-the-Art and Future Development -- Inverse Problems for Discrete Evolution Models -- Recent |
Developments in Electrical Impedance Tomography -- Two Inverse Problems for the Exponential Radon Transform -- Tomographic Image Reconstruction from a Limited Set of Projections Using a Natural Pixel Decomposition -- Application of the | |
Simulated Annealing Technique to Microwave Tomography: Preliminary Results -- Elastic Wave Diffraction Tomography -- II Distributed Parameters Inverse Problems -- Non-linear Least-Square Theory for Inverse Problems -- Circulant | |
Preconditioners for Non-negatively Constrained Deconvolution Problems -- Tikhonov Regularization of Nonlinear Differential-Algebraic Equations -- On the Choice of the Regularization Parameter Using Model Functions -- Exact | |
Reconstruction Procedures for Some Multidimensional Inverse Scattering and Inverse Boundary Value Problems -- On the Discretization and Regularization of Selfadjoint Ill-Posed Problems -- Age Structured Population Dynamics -- Ball | |
Stabilization in Inverse Problems -- III Spectral Inverse Problems -- Algorithms for Solving Inverse Eigenvalue Problems for Sturm-Liouville Equations -- Inverse Problem in the Coupling Constant -- Examples of Inverse Nodal Problems -- | |
Conditions on the Data in Inverse Problems in Vibration -- An Inverse Eigenvalue Problem and an Extremal Eigenvalue Problem -- IV Scattering Inverse Problems (Exact Methods) -- Scattering by Black-Hole for Electromagnetic Fields -- | |
Phase Space and Functional Integral Methods in Direct and Inverse Scattering -- New Results on 3D Schrödinger Inverse Scattering -- Electromagnetic Inverse Problems at Low Frequencies -- Retrieval of a Time-Dependent Source in an | |
Acoustic Propagation Problem -- Inverse Scattering Problems for the Wave Equation with Time Dependent Impurities -- Wave Splitting and the Reflection Operator for the Wave Equation -- Multidimensional Inverse Quantum Scattering Problem | |
and Wiener-Hopf Factorization -- The Direct and Inverse Scattering Transforms for a Sturm-Liouville Equation on Finite Interval as Smooth Maps. The Geometry of a Set of Finitely-Zoned Potentials -- V Theoretical Imaging -- Application | |
of Singular Systems to Some Data Reduction Problems in Modern Optics -- Temporal Homogenization -- Reciprocity, Discretization, and the Numerical Solution of Direct and Inverse Acoustic Radiation and Scattering Problems -- A Quadratic | |
Inverse Problem: The Phase Retrieval -- VI Wave Propagation and Scattering Problems (Imaging and Numerical Methods) -- Numerical Investigation of the Probing of Sea-Bottoms Using Exact and Approximate Methods -- Quantitative | |
Reconstruction of Complex Permittivity Distributions by Means of Microwave Tomography -- Some Asymptotic Results on Coherent-State Matrix Elements -- Inverse Problems for Dispersive Biological Media -- Image Estimation from Scattered | |
Field Data (at 10 GHz) Using the Distorted Wave Born Approximation and Other Prior Knowledge -- Phase Equivalence Between Nonlocal and Local Potentials Using Inversion and Supersymmetry -- Inverse Scattering Theory for Phase-Conjugate | |
Reflection Coefficients: Application to Optical Switching -- An Inverse Problem in Propellant Combustion -- Inversion of Three-Quark Spectral Data -- Stability and Convergence in the ID Time-Dependent Problem -- Inverse Profiling for | |
an Inhomogeneous, Plane-Stratified Lossy Causal Medium -- VII Miscellaneous Problems -- Some Remarks on the Relationship Between Mathematics and Physics and on Inverse Problems -- Variational Averaging of Problems with Stochastic Data | |
-- Some High Energy Cross Sections from an Inverse Point of View -- Exact Shock Wave Solutions for an 8v? Discrete Boltzmann Model with Temperature -- Teaching Direct and Inverse Problems by Means of User Friendly Interfaces: A Status | |
Report -- Quantum Inverse Scattering Theory and Nucleon-Nucleon Potentials -- Generalized Backus-Gilbert Methods -- Inversion of Ionospheric Sounding Data from an HF Backscatter Radar -- Generalized Bargmann-Type Potentials -- Rigorous | |
Computer Solutions of Infinite-Dimensional Inverse Problems -- Seismic Waveform Inversion Using a Layer-Stripping Method -- Highly Dimensional, Highly Non-linear Inverse Problems in Geophysics -- Numerical Construction of Nonlinear | |
Wave Train Solutions of the Periodic Korteweg-de Vries Equation -- VIII Inverse Methods and Applications to Nonlinear Problems -- The Meld Factorization in Relation to Various Problems in Mathematical Physics -- Some Ideas on Nonlinear | |
Evolution Equations -- Painlevé Singular Manifold Equation and Integrability -- The Davey-Stewartson 1 Equation: A Class of Explicit Solutions Including the Special Case of the Dromions -- The “IST” as a Diagnostic Tool for Perturbed | |
Nonlinear Schrödinger Systems -- Gaps of One-Dimensional Periodic AKNS Systems -- Combinatorial Aspects of Some Classes of Linearizable and Bilinearizable NLPDEs -- An Integrable Model for Small Amplitude Nonlinear Coupled Waves | |
Produced During Laser-Plasma Interaction -- On the Spectral Theory of the Davey-Stewartson Equation -- Multidimensional Solitons in Terms of Fermions -- On the AMCP Functional Equation for the Solvable Chiral Potts Model -- | |
Painlevé-Darboux Transformation in Nonlinear PDEs -- Solitons and Spectral Transform for the Kadomtsev-Petviashvili Equation -- Dromions, a New Manifestation in Nonlinear Phenomena -- The Phoenix Equation -- On the Dressing Method -- | |
Index of Contributors -- Conference Program | |
ISBN: | 9783642752988 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
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Keywords: | Physics , Physics , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-1989-9783642840005:ONLINE Show nearby items on shelf |
Title: | Problems of Modern Quantum Field Theory Invited Lectures of the Spring School held in Alushta USSR, April 24 – May 5, 1989 |
Author(s): | |
Date: | 1989 |
Size: | 1 online resource (157 p.) |
Note: | 10.1007/978-3-642-84000-5 |
Contents: | Quasi-Hopf Algebras and Knizhnik-Zamolodchikov Equations -- Quantum Lie Superalgebras and Supergroups -- From Geometric Quantization to Conformal Field Theory -- Bosonization of Wess-Zumino-Witten Models and Related Conformal Theories |
-- The Cutting and Sewing Method in String Theory -- P-Adic String World Sheets: Higher Genera -- Virasoro Action on Riemann Surfaces, Grassmannians, det $${\bar \partial _J}$$ and Segal-Wilson ?-Function -- On the Superextension of | |
the Kadomtsev-Petviashvili Equation and Finite-Gap Solutions of Korteweg-de Vries Superequations -- Finite Size Effects in Conformal Field Theories and Non-local Operators in One-Dimensional Quantum Systems -- The Solution of the | |
Two-Dimensional Ising Model with Magnetic Fields Applied to the Boundaries -- On the Relativistic Field Theories with Fractional Statistics and Spin in D=(2+1), (3+1) -- Electron on a Surface in an External Magnetic Field: Hidden | |
Supersymmetry, Zero Modes and Boundary Conditions -- Index of Contributors | |
ISBN: | 9783642840005 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Quantum physics , Elementary particles (Physics) , Quantum field theory , Condensed matter , Quantum computers , Spintronics , Statistical physics , Dynamical systems , Physics , Quantum Physics , Elementary Particles, Quantum Field Theory , Statistical Physics, Dynamical Systems and Complexity , Condensed Matter Physics , Quantum Information Technology, Spintronics |
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Call number: | SPRINGER-1989-9781475720631:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods of Classical Mechanics |
Author(s): |
V. I Arnold |
Date: | 1989 |
Edition: | Second Edition |
Size: | 1 online resource (520 p.) |
Note: | 10.1007/978-1-4757-2063-1 |
Contents: | I Newtonian Mechanics -- 1 Experimental facts -- 2 Investigation of the equations of motion -- II Lagrangian Mechanics -- 3 Variational principles -- 4 Lagrangian mechanics on manifolds -- 5 Oscillations -- 6 Rigid bodies -- III |
Hamiltonian Mechanics -- 7 Differential forms -- 8 Symplectic manifolds -- 9 Canonical formalism -- 10 Introduction to perturbation theory -- Appendix 1 Riemannian curvature -- Appendix 2 Geodesics of left-invariant metrics on Lie | |
groups and the hydrodynamics of ideal fluids -- Appendix 3 Symplectic structures on algebraic manifolds -- Appendix 4 Contact structures -- Appendix 5 Dynamical systems with symmetries -- Appendix 6 Normal forms of quadratic | |
hamiltonians -- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories -- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov’s theorem -- Appendix 9 Poincaré’s | |
geometric theorem, its generalizations and applications -- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters -- Appendix 11 Short wave asymptotics -- Appendix 12 Lagrangian singularities | |
-- Appendix 13 The Korteweg-de Vries equation -- Appendix 14 Poisson structures -- Appendix 15 On elliptic coordinates -- Appendix 16 Singularities of ray systems | |
ISBN: | 9781475720631 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 60 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Physics , Mathematics , Analysis , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-1987-9781461395836:ONLINE Show nearby items on shelf |
Title: | Wave Motion: Theory, Modelling, and Computation Proceedings of a Conference in Honor of the 60th Birthday of Peter D. Lax |
Author(s): | |
Date: | 1987 |
Size: | 1 online resource (336 p.) |
Note: | 10.1007/978-1-4613-9583-6 |
Contents: | Lattice Vortex Models and Turbulence Theory -- The Curve Shortening Flow -- Lax’s Construction of Parametrices of Fundamental Solutions of Strongly Hyperbolic Operators, Its Prehistory and Posthistory -- The Bukiet-Jones Theory of |
Weak Detonation Waves in Curvilinear Geometry -- Three-Dimensional Fluid Dynamics in a Two-Dimensional Amount of Central Memory -- On the Nonlinearity of Modern Shock-Capturing Schemes -- High Frequency Semilinear Oscillations -- Exact | |
Controllability and Singular Perturbations -- Transonic Flow and Compensated Compactness -- Scattering Theory for the Wave Equation on a Hyperbolic Manifold -- Determinants of Laplacians on Surfaces -- The Small Dispersion Limit of the | |
Korteweg-de Vries Equation | |
ISBN: | 9781461395836 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematical Sciences Research Institute Publications: 7 |
Keywords: | Physics , Physics , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-1986-9783540473879:ONLINE Show nearby items on shelf |
Title: | Asymptotic Analysis of Soliton Problems An Inverse Scattering Approach |
Author(s): |
Peter Cornelis Schuur |
Date: | 1986 |
Size: | 1 online resource (182 p.) |
Note: | 10.1007/BFb0073054 |
Contents: | The emergence of solitons of the Korteweg-de Vries equation from arbitrary initial conditions -- Asymptotic estimates of solutions of the Korteweg-de Vries equation on right half lines slowly moving to the left -- Multisoliton phase |
shifts for the korteweg-de vries equation in the case of a nonzero reflection coefficient -- On the approximation of a real potential in the Zakharov-Shabat system by its reflectionless part -- Decomposition and estimates of solutions | |
of the modified Korteweg-de Vries equation on right half lines slowly moving leftward -- Multisoliton phase shifts for the modified Korteweg-de Vries equation in the case of a nonzero reflection coefficient -- Asymptotic estimates of | |
solutions of the Sine-Gordon equation on right half lines almost linearly moving leftward -- On the approximation of a complex potential in the Zakharov-Shabat system by its reflectionless part | |
ISBN: | 9783540473879 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1232 |
Keywords: | Physics , Physics , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-1983-9781461255611:ONLINE Show nearby items on shelf |
Title: | Semigroups of Linear Operators and Applications to Partial Differential Equations |
Author(s): |
A Pazy |
Date: | 1983 |
Size: | 1 online resource (282 p.) |
Note: | 10.1007/978-1-4612-5561-1 |
Contents: | 1 Generation and Representation -- 1.1 Uniformly Continuous Semigroups of Bounded Linear Operators -- 1.2 Strongly Continuous Semigroups of Bounded Linear Operators -- 1.3 The Hille-Yosida Theorem -- 1.4 The Lumer Phillips Theorem -- |
1.5 The Characterization of the Infinitesimal Generators of C0 Semigroups -- 1.6 Groups of Bounded Operators -- 1.7 The Inversion of the Laplace Transform -- 1.8 Two Exponential Formulas -- 1.9 Pseudo Resolvents -- 1.10 The Dual | |
Semigroup -- 2 Spectral Properties and Regularity -- 2.1 Weak Equals Strong -- 2.2 Spectral Mapping Theorems -- 2.3 Semigroups of Compact Operators -- 2.4 Differentiability -- 2.5 Analytic Semigroups -- 2.6 Fractional Powers of Closed | |
Operators -- 3 Perturbations and Approximations -- 3.1 Perturbations by Bounded Linear Operators -- 3.2 Perturbations of Infinitesimal Generators of Analytic Semigroups -- 3.3 Perturbations of Infinitesimal Generators of Contraction | |
Semigroups -- 3.4 The Trotter Approximation Theorem -- 3.5 A General Representation Theorem -- 3.6 Approximation by Discrete Semigroups -- 4 The Abstract Cauchy Problem -- 4.1 The Homogeneous Initial Value Problem -- 4.2 The | |
Inhomogeneous Initial Value Problem -- 4.3 Regularity of Mild Solutions for Analytic Semigroups -- 4.4 Asymptotic Behavior of Solutions -- 4.5 Invariant and Admissible Subspaces -- 5 Evolution Equations -- 5.1 Evolution Systems -- 5.2 | |
Stable Families of Generators -- 5.3 An Evolution System in the Hyperbolic Case -- 5.4 Regular Solutions in the Hyperbolic Case -- 5.5 The Inhomogeneous Equation in the Hyperbolic Case -- 5.6 An Evolution System for the Parabolic | |
Initial Value Problem -- 5.7 The Inhomogeneous Equation in the Parabolic Case -- 5.8 Asymptotic Behavior of Solutions in the Parabolic Case -- 6 Some Nonlinear Evolution Equations -- 6.1 Lipschitz Perturbations of Linear Evolution | |
Equations -- 6.2 Semilinear Equations with Compact Semigroups -- 6.3 Semilinear Equations with Analytic Semigroups -- 6.4 A Quasilinear Equation of Evolution -- 7 Applications to Partial Differential Equations—Linear Equations -- 7.1 | |
Introduction -- 7.2 Parabolic Equations—L2 Theory -- 7.3 Parabolic Equations—Lp Theory -- 7.4 The Wave Equation -- 7.5 A Schrödinger Equation -- 7.6 A Parabolic Evolution Equation -- 8 Applications to Partial Differential | |
Equations—Nonlinear Equations -- 8.1 A Nonlinear Schröinger Equation -- 8.2 A Nonlinear Heat Equation in R1 -- 8.3 A Semilinear Evolution Equation in R3 -- 8.4 A General Class of Semilinear Initial Value Problems -- 8.5 The Korteweg-de | |
Vries Equation -- Bibliographical Notes and Remarks | |
ISBN: | 9781461255611 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Applied Mathematical Sciences: 44 |
Keywords: | Mathematics , Group theory , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis , Group Theory and Generalizations |
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Call number: | SPRINGER-1982-9783642817489:ONLINE Show nearby items on shelf |
Title: | Elastic Media with Microstructure I One-Dimensional Models |
Author(s): |
Isaak A Kunin |
Date: | 1982 |
Size: | 1 online resource (296 p.) |
Note: | 10.1007/978-3-642-81748-9 |
Contents: | 1 Introduction -- 2 Medium of Simple Structure -- 2.1 Simple Chain -- 2.2 One-Dimensional Quasicontinuum -- 2.3 One-Dimensional Quasicontinuum (continued) -- 2.4 Equation of Motion and Elastic Energy Operator -- 2.5 Strain and Stress, |
Energy Density, and Energy Flux -- 2.6 Boundary Problems -- 2.7 The Dispersion Equation -- 2.8 Kernel of Operator ?? in the Complex Region -- 2.9 Green’s Function and Structure of the General Solution -- 2.10 Approximate Models -- 2.11 | |
Solution of Basic Boundary Problems -- 2.12 Notes -- 3 Medium of Complex Structure -- 3.1 Basic Micromodels -- 3.2 Collective Cell Variables -- 3.3 Phenomenology -- 3.4 Acoustical and Optical Modes of Vibration. General Solution and | |
Green’s Matrix -- 3.5 Long-Wave Approximation and Connection with One-Dimensional Analog of Couple-Stress Theories -- 3.6 Elimination of the Internal Degrees of Freedom in the Acoustic Region -- 3.7 Equivalent Medium of Simple | |
Structure -- 3.8 Diatomic Chain -- 3.9 The Cosserat Model -- 3.10 Notes -- 4 Nonstationary Processes -- 4.1 Green’s Functions of the Generalized Wave Equation -- 4.2 Investigation of the Asymptotics Behavior -- 4.3 Decomposition into | |
Packets and Factorization of Wave Equations -- 4.4 Energy Method and Quantum-Mechanical Formalism -- 4.5 Characteristics of the Evolution of a Packet -- 4.6 Superposition of Packets -- 4.7 Solutions Localized in the Neighborhood of | |
Extrema of the Dispersion Curve -- 4.8 The Case of External Forces -- 4.9 Weakly Inhomogeneous Medium -- 4.10 Local Defects -- 4.11 The Structure of the Green’s Function of an Inhomogeneous Medium -- 4.12 The Scattering Matrix -- 4.13 | |
Connection of the S-Matrix with Green’s Functions -- 4.14 Scattering on Local Defects -- 4.15 Notes -- 5 Nonlinear Waves -- 5.1 Korteweg-de Vries Model -- 5.2 Connection Between the KdV-Model and Nonlinear Wave Equation -- 5.3 Deformed | |
Soliton -- 5.4 The Nonlinear Chain -- 5.5 Conservation Laws -- 5.6 Decay of the Initial Perturbation and the Distribution Function of Solitons -- 5.7 The Soliton Gas -- 5.8 Notes -- 6 Inverse Scattering Method -- 6.1 Basic Idea of the | |
Method -- 6.2 Inverse Scattering Problem for the Operator L = d2/dx2 + u(x) -- 6.3 N-Soliton Solutions of the KdV-Equation -- 6.4 Complete Integrability of the KdV-Equation -- 6.5 Shabat’s Method -- 6.6 N-Soliton Solutions for the | |
Equation of Nonlinear String -- 6.7 The Toda Lattice -- 6.8 Fermi-Pasta-Ulam Problem -- 6.9 Perspectives of the Method -- 6.10 Notes -- Appendices -- 1. Summary of Fourier Transforms -- 2. Retarded Functions and Dispersion Relations -- | |
3. Expansion of Functions, Given at a Finite Number of Points, in Special Bases -- References | |
ISBN: | 9783642817489 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Series in Solid-State Sciences: 26 |
Keywords: | Physics , Mechanics , Physics , Mechanics |
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Call number: | SPRINGER-1981-9783642815096:ONLINE Show nearby items on shelf |
Title: | Solitons Mathematical Methods for Physicists |
Author(s): |
Gert Eilenberger |
Date: | 1981 |
Size: | 1 online resource (194 p.) |
Note: | 10.1007/978-3-642-81509-6 |
Contents: | 1. Introduction -- 1.1 Why Study Solitons? -- 1.2 Basic Concepts Illustrated by Simple Examples -- 2. The Korteweg-de Vries Equation (KdV-Equation) -- 2.1 The Physical Meaning of the KdV Equation -- 2.2 The KdV Equation as a |
Lagrangian Field Theory: Symmetries -- 2.3 Local Conservation Laws for the KdV System -- 2.4 Simple Solutions of the KdV Equation -- 3. The Inverse Scattering Transformation (IST) as Illustrated with the KdV -- 3.1 The Linear | |
Eigenvalue Problem -- 3.2 Commutation Relations for (KdV)n -- 3.3 Inverse Scattering Theory of Gel'fand-Levitan-Marchenko -- 3.4 Application to the KdV Equation: N Soliton Solution -- 3.5 Squared-Function Systems, or: the Secret of the | |
KdV Equation -- 3.6 Dynamics of the Scattering Data -- 3.7 Birth and Death of Solitons -- 4. Inverse Scattering Theory for Other Evolution Equations -- 4.1 Statement of the Problem -- 4.2 Inverse Scattering Theory for Equation (4.1.1) | |
-- 4.3 Orthogonal Systems of Functions, Associated Operators, and Induced Poisson Brackets -- 4.4 Further Nonlinear Evolution Equations -- 4.5 The Simplest Nonpolynomial “Dispersion Relations” -- 4.6 Time Development of the Scattering | |
Data -- 4.7 Transformation Theory: Miura and Bäcklund Transformations -- 4.8 Perturbation Theory and Stability -- 4.9 Summary of Results, Problems, and Simple Extension to Higher Dimensions -- 5. The Classical Sine-Gordon Equation | |
(SGE) -- 5.1 Basic Equations -- 5.2 Soliton Solutions of the SGE -- 5.3 Simple Solutions of the PSG -- 5.4 Cauchy Problem for the PSG and Particle Representation -- 5.5 PSG Solitons in the Presence of External Perturbations -- 5.6 | |
Possible Generalizations -- 6. Statistical Mechanics of the Sine-Gordon System -- 6.1 Functional Integrals -- 6.2 Partition Function in the Soliton Picture -- 6.3 Partition Function by a Scale Transformation -- 7. Difference Equations: | |
The Toda Lattice -- 7.1 Basic Considerations -- 7.2 IST for the Toda Lattice -- 7.3 Systems of Squared Functions -- 7.4 Soliton Solutions for the Toda Lattice -- References | |
ISBN: | 9783642815096 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Series in Solid-State Sciences: 19 |
Keywords: | Physics , Physics , Mathematical Methods in Physics , Numerical and Computational Physics |
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Call number: | SPRINGER-1980-9783540391975:ONLINE Show nearby items on shelf |
Title: | Nonlinear Evolution Equations and Dynamical Systems Proceedings of the Meeting Held at the University of Lecce June 20–23, 1979 |
Author(s): | |
Date: | 1980 |
Size: | 1 online resource (370 p.) |
Note: | 10.1007/3-540-09971-9 |
Contents: | Nonlinear evolution equations solvable by the spectral transform: Some recent results -- Quantization of completely integrable Hamiltonian systems -- Reduction technique for matrix nonlinear evolution equations -- Similarity solutions |
of the korteweg-de vries equation, Bäclund transformations and painlevè transcendents -- Coadjoint structures, solitions, and integrability -- Around the classical string problem -- The generalized Riemann-Hilbert problem and the | |
spectral interpretation -- The inverse scattering problem and applications to arithmetics, approximation theory and transcendental numbers -- The soliton theory of strong langmuir turbulence -- Geometry of bäcklund transformations -- | |
Existence of solutions and scattering theory for the non linear schrödinger equation -- A geometrical approach to the nonlinear solvable equations -- Properties of a special function related to self-similar solutions of certain | |
nonlinear wave equations -- Vortex motions and conformal mappings -- Analytical solutions of the sine-gordon equation and their application to josephson tunnel junctions -- Geometry of the akns — ZS inverse scattering scheme -- | |
Fundamental equations of classical and of quantum physics as special cases of a nonlinear equation -- Noether's theorem and infinities of polynomial conserved densities | |
ISBN: | 9783540391975 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Physics: 120 |
Keywords: | Physics , Physics , Mathematical Methods in Physics , Numerical and Computational Physics |
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Call number: | SPRINGER-1978-9789400998919:ONLINE Show nearby items on shelf |
Title: | Nonlinear Equations in Physics and Mathematics Proceedings of the NATO Advanced Study Institute held in Istanbul, Turkey, August 1–13, 1977 |
Author(s): | |
Date: | 1978 |
Size: | 1 online resource (474 p.) |
Note: | 10.1007/978-94-009-9891-9 |
Contents: | I - Dynamical Systems and Inverse Scattering Problems -- Integrable Many-Body Problems -- Inverse Scattering Problems for Nonlinear Applications -- Solutions of Nonlinear Equations Simulating Pair Production and Pair Annihilation -- |
The Two-Time Method Applied to Slowly Evolving Oscillating Systems -- II - Solitons -- Solitons in Physics -- Solitons and Geometry -- Hirota’s Method of Solving Soliton-Type Equations -- Prolongation Structure Techniques for the New | |
Hierarchy of Korteweg-de Vries Equations -- Perturbation Theory for the Double Sine-Gordon Equation -- III - Discrete Systems and Continuum Mechanics -- Painlevé Transcendents and Scaling Functions of the Two-Dimensional Ising Model -- | |
Statistical Mechanics of Nonlinear Lattice Dynamic Models Exhibiting Phase Transitions -- Nonlocal Continuum Mechanics and Some Applications -- IV - Nonlinear Field Theories and Quantization -- Quantization of a Nonlinear Field | |
Equation -- Characteristic “Quanta” of Nonlinear Field Equations -- Nonlinear Schrödinger Equation with Sources: An Application of the Canonical Formalism -- Nonlinear Field Equations and Collective Phenomena -- Nonperturbative | |
Self-Interactions, Solitary Waves and Others -- Bound States of Fermions in External and Self-Consistent Fields | |
ISBN: | 9789400998919 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | NATO Advanced Study Institutes Series, Series C - Mathematical and Physical Sciences: 40 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis |
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Call number: | SPRINGER-1978-9783642812910:ONLINE Show nearby items on shelf |
Title: | Solitons and Condensed Matter Physics Proceedings of the Symposium on Nonlinear (Soliton) Structure and Dynamics in Condensed Matter, Oxford, England, June 27–29, 1978 |
Author(s): | |
Date: | 1978 |
Size: | 1 online resource (344 p.) |
Note: | 10.1007/978-3-642-81291-0 |
Contents: | I. Introduction -- Solitons in Mathematics: Brief History -- Solitons in Physics -- II. Mathematical Aspects -- Numerical Studies of Solitons -- Poles of the Toda Lattice -- Perturbation Theory of the Double Sine-Gordon Equation -- |
Soliton Perturbations and Nonlinear Focussing -- Novel Class of Nonlinear Evolution Equations Solvable by the Spectral Transform Technique, Including the So-Called Cylindrical KdV Equation -- The Complex Modified Korteweg-de Vries | |
Equation, a Non-Integrable Evolution Equation -- III. Statistical Mechanics and Solid-State Physics -- Soliton-Bound States in the Magnetic Gap -- Statistical Mechanics of Nonlinear Dispersive Systems -- Some Applications of Instantons | |
in Statistical Mechanics -- The Theory of Structural Phase Transitions: Cluster Walls and Phonons -- Nonlinear Lattice Dynamics: Molecular Dynamics Studies -- Computer Simulation of Structural Phase Transitions -- Soliton-Like Features | |
in a Two-Dimensional XY Model with Ouartic Anisotropy -- Behavior of a ?4-Kink in the Presence of an Inhomogeneous Perturbation -- Solitary Wave Solutions in a Diatomic Lattice -- Lattice Models of High Velocity Dislocation Motion -- | |
Grain Boundaries as Solitary Waves -- The Relation of Solitons to Polaritons in Coupled Systems -- Solitons in CsNiF3: Their Experimental Evidence and Their Thermodynamics -- Structure and Stability of Domain Walls — Phase Transition | |
-- Periodic Lattice Distortions and Charge Density Waves in One- and Two-Dimensional Systems -- Solitons in Incommensurate Systems -- Fluctuations and Freezing in a One-Dimensional Liquid: Hg3??AsF6 -- Charge Density Wave Systems: The | |
?-Particle Model -- The Soliton Lattice: Application to the ? Phase -- The New Concept of Transitions by Breaking of Analyticity in a Crystallographic Model -- Textures in Superfluid 3He -- Creation of Spin Waves in 3HeB -- The | |
Interaction of Spin Waves in Liquid He3 in Several Dimensions -- Josephson Transmission Line Oscillators -- Dissipative Structures in Quasi-One-Dimensional Superconductors -- Solitary Phenomena in Finite Dissipative Discrete Systems -- | |
Stability of Nonuniform States in Systems Exhibiting Continuous Bifurcation -- The Sine-Gordon Chain: Mass Diffusion -- Solitary-Wave Propagation as a Model for Poling in PVF2 -- Theory of One-Dimensional Ionic and Solitary Wave | |
Conduction in Potassium Hollandite -- IV. Summary -- Summary: Where Do Solitons Go From Here? -- Index of Contributors | |
ISBN: | 9783642812910 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Series in Solid-State Sciences: 8 |
Keywords: | Physics , Physics , Mathematical Methods in Physics , Numerical and Computational Physics |
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Call number: | SPRINGER-1978-9781475716931:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods of Classical Mechanics |
Author(s): |
V. I Arnold |
Date: | 1978 |
Size: | 1 online resource (464 p.) |
Note: | 10.1007/978-1-4757-1693-1 |
Contents: | I Newtonian Mechanics -- 1 Experimental facts -- 2 Investigation of the equations of motion -- II Lagrangian Mechanics -- 3 Variational principles -- 4 Lagrangian mechanics on manifolds -- 5 Oscillations -- 6 Rigid Bodies -- III |
Hamiltonian Mechanics -- 7 Differential forms -- 8 Symplectic manifolds -- 9 Canonical formalism -- 10 Introduction to perturbation theory -- Appendix 1 Riemannian curvature -- Appendix 2 Geodesies of left-invariant metrics on Lie | |
groups and the hydrodynamics of an ideal fluid -- Appendix 3 Symplectic structure on algebraic manifolds -- Appendix 4 Contact structures -- Appendix 5 Dynamical systems with symmetries -- Appendix 6 Normal forms of quadratic | |
hamiltonians -- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories -- Appendix 8 Perturbation theory of conditionally periodic motions and Kolmogorov’s theorem -- Appendix 9 Poincaré’s | |
geometric theorem, its generalizations and applications -- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters -- Appendix 11 Short wave asymptotics -- Appendix 12 Lagrangian singularities | |
-- Appendix 13 The Korteweg-de Vries equation | |
ISBN: | 9781475716931 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 60 |
Keywords: | Mathematics , Mathematics , Mathematics, general |
Availability: | Click here to see Library holdings or inquire at
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Call number: | QA377.K367::2010 Show nearby items on shelf |
Title: | Glimpses of soliton theory: The algebra and geometry of nonlinear PDEs |
Author(s): |
Alex Kasman |
Date: | 2010 |
Publisher: | Providence, R.I.: American Mathematical Society |
Size: | 304 p. |
Contents: | Differential equations, Developing PDE intuition, The story of solitons, Elliptic curves and KdV traveling waves, KdV -solitons, Multiplying and factoring differential operators Eigenfunctions and isospectrality, Lax form for KdV and other soliton equ ations, The KP equation and bilinear KP equation, The Grassmann cone Γ_{2,4} and the bilinear KP equation Pseudo-differential operators and the KP hierarchy, The Grassman cone and the bilinear KP hierarchy, Concluding remarks, Mathematica guide, Complex numbers, Ideas for independent projects |
ISBN: | 9780821852453 |
Series: | Student mathematical library, v. 54. |
Keywords: | Korteweg-de Vries equation. , Geometry, Algebraic. , Differential equations, Partial. |
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here to see Library holdings or inquire at Circ Desk (x3401)
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Location: | MAIN |
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