Nonlinear Physics

InhaltsangabeI Integrable Systems: Hamiltonian Structure, Symmetries, Bäcklund and Darboux Transformations.- Liouville Integrability of Zero Curvature Equations.- 2+1 Dimensional Integrable Hierarchies, Lax Operators and Relevant Algebraic Structures.- Determination of Nondegenerate Darboux Operators of First Order in 1+2 Dimensions.- A Series of New Exact Solutions to the Nonlinear Equation yt+yxxx? 6y2yx+6?yx=0.- Bäcklund Transformations for the Isospectral and Non-Isospectral KdV Hierarchies.- Multiple Darboux Transformations and Multiple Pole Solutions for AKNS Hierarchy.- A Lie Algebraic Structure of G J. and Its Gauge Equivalent Yang Hierarchies.- II Finite Dimensional Dynamical Systems.- Coupled Nonlinear Oscillators: Symmetries and Integrability.- Classical Integrable Systems Generated Through Nonlinearization of Eigenvalue Problems.- The Confocal Involutive System and the Integrability of the Nonlinearized Lax Systems of AKNS Hierarchy.- Two Kinds of Finite-Dimensional Systems Related to the Generalized Schrödinger Equation.- Nonlinearization of the Lax Pair for the KdV Equation and Integrable Hamiltonian Systems.- III Quantum Aspects and Statistical Mechanics.- Quantum and Classical Statistical Mechanics of the Integrable Models in 1 + 1 Dimensions.- Link Polynomials and Exactly Solvable Models.- R-Matrices and Higher Poisson Brackets for Integrable Systems.- Classical R-Matrix and Semi-Simple Lie Algebras.- Witten's Approach, Braid Group Representations and X-Deformations.- IV Physical Phenomena.- Nonlinear Evolution Equations, Solitons, Chaos and Cellular Automata.- Kadomtsev-Petviashvili Equations in the Description of Water Waves.- Three-Dimensional Lattice Model Based on Soliton Theory.- Soliton Phenomena in a Porous Medium.- Two-Dimensional Chiral Gauge Theories on a Lattice.- Transformation for the Solutions of the Two-Dimensional Toda Lattice.- V Other Topics.- Some Ideas on Nonlinear Evolution Equations.- Some Problems of the Generalized Kuramoto-Sivashinsky Type Equations with Dispersive Effects.- Standard Nonlinearities Associated with KdV-like Two-Soliton Solutions.- Complex Singularities and the Riemann Surface for the Burgers Equation.- From Soliton Theory to String Theory.- Non-Linear Equations from a String-Theoretical Point of View.- Painlevé Analysis and Integrability of the Evolution Equation ut=uxxx+u2uxx+3uux2+l/3u4ux.- List of Participants.- Index of Contributors.