Symmetries and Singularity Structures: Integrability and Chaos in Nonlinear Dynamical Systems

by Muthuswamy Lakshmanan (Editor), Muthiah Daniel (Editor)

Overview

These lectures deal with background and latest developments in symmetries, singularity structures (Painlevé analysis) and their relation to integrability and chaos in classical and quantum nonlinear dynamical systems. The book is useful to both newcomers and senior researchers in physics and mathematics working in the field of nonlinear dynamics. Starting from simple Lie symmetries the role of generalized Lie and Lie-Bäcklund symmetries and the underlying algebras associated with a wide spectrum of nonlinear systems are studied. Some keywords are: Master symmetries, dynamical symmetries, Kac-Moody and Virasoro algebras, quantum groups, integrable quantum spin chains, bi-Hamiltonian structure of integrable systems and singularity structure analysis of Hamiltonian and non-Hamiltonian systems, the connection between symmetry, solitons, quantum chaos and random matrix theory, applications of solitons in plasmas, 4He films, Josephson junctions and in chemical compounds.

Product Details

ISBN-13:	9783540530923
Publisher:	Springer Berlin Heidelberg
Publication date:	02/13/1991
Series:	Research Reports in Physics
Edition description:	Softcover reprint of the original 1st ed. 1990
Pages:	208
Product dimensions:	6.69(w) x 9.53(h) x 0.02(d)

Table of Contents

I Symmetry Aspects.- Symmetries, Singularities and Exact Solutions for Nonlinear Systems.- Application of Isovector Approach for the Solutions of Differential Equations of Physical Systems.- Master Symmetries of Certain Nonlinear Partial Differential Equations.- Symmetries and Constants of Motion of Integrable Systems.- Lie Algebra, Bi-Hamiltonian Structure and Reduction Problem for Integrable Nonlinear Systems.- On the Role of Virasoro, Kac-Moody Algebra and Conformal Invariance in Soliton Hierarchies.- Generalised Lie Symmetries and Integrability of Coupled Nonlinear Oscillators with Two Degrees of Freedom.- Aspects of Symmetries of Dissipative Systems.- II Singularity Structure Aspects.- Painlevé Property in Hamiltonian and Non-Hamiltonian Systems.- Singularity Structure and Chaotic Dynamics of the Parametrically Driven Duffing Oscillator.- A Singularity Analysis Approach to the Solutions of Duffing’s Equation.- III Integrability and Chaos: Quantum and Classical.- Avoided Level Crossing, Solitons and Random Matrix Theory.- Random Matrices and Quantum Chaos: Effects of Symmetry-Breaking on Spectral Correlations.- Quantum Groups.- Integrable Quantum Spin Chains and Some Problems Related to Integrable Systems.- On the Quantum Inverse Problem for a New Type of Nonlinear Schrödinger Equation for Alfven Waves in Plasma.- Nonlinear Chemical Dynamics.- Dynamics of Solitons on 4He Films.- Studies on a Josephson Junction with Nonlinear Resistance.- Index of Contributors.