Nonlinear Evolution Equations and Dynamical Systems [Paperback]

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: Painlev? Property, Hirota Method, Lie-B?cklund Symmetries.- Examples of Nonclassical Similarity Reductions.- Equations That Pass Hirotas Three-Soliton Condition and Other Tests of Integrability.- Selection of Solvable Nonlinear Evolution Equations by Systematic Searches for Lie B?cklund 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 Painlev? Equation.- Nonlinear Equations for Soliton Eigenfunctions Are the IST Integrable Equations.- The Geometry and Completeness of the Two-Phase Solutions of the Nonlinear Schr?dinger 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 PDEs 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 lÈ