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SPIRES-BOOKS: FIND KEYWORD KORTEWEG-DE VRIES EQUATION *END*INIT* use /tmp/qspiwww.webspi1/8401.20 QRY 131.225.70.96 . find keyword korteweg-de vries equation ( in books using www Cover
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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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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
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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-1990-9783642840395: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
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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
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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
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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)
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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
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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)
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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
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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
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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
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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
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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.
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
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Location: MAIN

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