Integrability of Nonlinear Systems

The Editors (auth.), Yvette Kosmann-Schwarzbach, K. M. Tamizhmani, Basil Grammaticos (eds.)9783540206309, 3540206302

The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

Table of contents :
Introduction….Pages 1-4
Nonlinear Waves, Solitons, and IST….Pages 5-29
Integrability – and How to Detect It….Pages 31-94
Introduction to the Hirota Bilinear Method….Pages 95-105
Lie Bialgebras, Poisson Lie Groups, and Dressing Transformations….Pages 107-173
Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: A Review and Extensions of Tests for the Painlevé Property….Pages 175-208
Eight Lectures on Integrable Systems….Pages 209-250
Bilinear Formalism in Soliton Theory….Pages 251-268
Quantum and Classical Integrable Systems….Pages 269-333