Nonlinear Evolution Equations and Dynamical Systems: Needs '90

ISBN-13: 9783540532941 / Angielski / Miękka / 1991 / 240 str.

Vladimir G. Makhankov; Oktay K. Pashaev

Opis

This text considers nonlinear evolution equations and dynamical systems and provides a presentation of the state of the art. Amongst the topics considered are one- and multi-dimensional models, geometric and algebraic methods, quantum field theory and applications to nonlinear optics.

Spis treści

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.

O autorze

Oktay K. Pashaev Diploma in Physics-Moskow state university, Phd-JINR, Dubna: Proffessor of mathematics at IYTE. Field of study: Integrable systems, Solitons and Quantum physics.