Introduction to classical integrable systems

O. Babelon, D. Bernard and M. Talon

This page provides informations about this book which is to appear in 2003 at Cambridge University Press in the collection Cambridge monographs on Mathematical Physics.

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 provides comprehensive reference for researchers already working in the field.

To get an idea of the coverage, you can browse the table of contents and read the Introduction.

You are welcome to email any of the authors for any comments, especially if you discover misprints or errors.

Olivier Babelon
Denis Bernard
Michel Talon

Errata  will be published here.