Nonlinear Physics

These refereed proceedings present recent developments on specific mathematical and physical aspects of nonlinear dynamics. The new findings discussed in here will be equally useful to graduate students and researchers. The topics dealt with cover a wide range of phenomena: solitons, integrable systems, Hamiltonian structures, Bäcklund and Darboux transformation, symmetries, fi- nite-dimensional dynamical systems, quantum and statistical mechanics, knot theory and braid group, R-matrix method, Hirota and Painlevé analysis, and applications to water waves, lattices, porous media, string theory and even cellular automata.

Contenu

I 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.