Introduction to Classical Integrable Systems

Olivier Babelon, Denis Bernard, Michel Talon

608 pages, parution le 05/05/2003

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Résumé

This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems.
The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.

Contents

Introduction
Integrable dynamical systems
Synopsis of integrable systems
Algebraic methods
Analytical methods
The closed Toda chain
The Calogero-Moser model
Isomonodromic deformations
Grassmannian and integrable hierarchies
The KP hierarchy
The KdV hierarchy
The Toda field Theories
Classical inverse scattering method
Symplectic geometry
Riemann surfaces
Lie algebras

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Olivier Babelon, Denis Bernard, Michel Talon
Parution	05/05/2003
Nb. de pages	608
Format	18 x 25,5
Couverture	Relié
Poids	1181g
Intérieur	Noir et Blanc
EAN13	9780521822671
ISBN13	978-0-521-82267-1