Amit K. Roy-Chowdhury

Lie Algebraic Methods in Integrable Systems

• Broschiertes Buch

Produktbeschreibung

In recent decades, the study of nonlinear integrable systems has grown into a full-fledged research topic. The ideas associated with Lie algebra and groups can form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author presents the techniques for using Lie algebraic concepts to explore nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as a tool. The text summarizes the use of these methods in various fields of theoretical research and serves mathematicians and theoretical physicists working in nonlinear integrable systems, dynamical systems, and chaos.

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Produktdetails

• Verlag: Chapman and Hall/CRC
• Seitenzahl: 368
• Erscheinungstermin: 28. September 1999
• Englisch
• Abmessung: 234mm x 156mm x 20mm
• Gewicht: 559g
• ISBN-13: 9781584880370
• ISBN-10: 1584880376
• Artikelnr.: 21454910

Autorenporträt

Amit K. Roy-Chowdhury (University of California, Riverside, USA) (Author)

Inhaltsangabe

INTRODUCTION
Lax Equation and IST
Conserved Densities and Hamiltonian Structure
Symmetry Aspects
Observations
LIE ALGEBRA
Introduction
Structure Constants and Basis of Lie Algebra
Lie Groups and Lie Algebra
Representation of a Lie Algebra
Cartan-Killing Form
Roots Space Decomposition
Lie Groups: Finite and Infinite Dimensional
Loop Groups
Virasoro Group
Quantum Tori Algebra
Kac-Moody Algebra
Serre's Approach to Kac-Moody Algebra
Gradation
Other Infinite Dimensional Lie Algebras
PROLONGATION THEORY
Introduction
Sectioning of Forms
The KdV Problem
The Method of the Hall Structure
Prolongation in (2+1) Dimension
Method of Pseudopotentials
Prolongation Structure and the Backlund Transformation
Constant Coefficient Ideal
Connections
Morphisms and Prolongation
Principal Prolongation Structure
Prolongations and Isovectors
Vessiot's Approach
Observations
CO-ADJOINT ORBITS
Introduction
The Kac-Moody Algebra
Integrability Theorem: Adler
Kostant
Symes
Superintegrable Systems
Nonlinear Partial Differential Equation
Extended AKS Theorem
Space-Dependent Integrable Equation
The Moment Map
Moment Map in Relation to Integrable Nonlinear Equation
Co-Adjoint Orbit of the Volterra Group
SYMMETRIES OF INTEGRABLE SYSTEMS
Introduction
Lie Point and Lie Backlund Symmetry
Lie Backlund Transformation
Some New Ideas in Symmetry Analysis
Non-Local Symmetries
Observations
HAMILTONIAN STRUCTURE
Introduction
Drinfeld Sokolob Approach
The Lie Algebraic Approach
Example of Hamiltonian Structure and Reduction
Hamiltonian Reduction in (2+1) Dimension
Hamiltonian Reduction of Drinfeld and Sokolov
Kupershmidt's Approach
Gelfand Dikii Formula
Trace Identity and Hamiltonian Structure
Symmetry and Hamiltonian Structure
CLASSICAL r-MATRIX
Introduction
Double Lie Algebra
Classical r-Matrix
The Use of r-Matrix
The r-Matrix and KP Equation