Integrability of Nonlinear Systems: Proceedings of the CIMPA School Pondicherry University, India, 8–26 January 1996

Y. Kosmann-Schwarzbach, B. Grammaticos, K. M. Tamizhmani (eds.)9783540633532, 3540633537

The theory of nonlinear systems and, in particular, of integrable systems is related to several very active fields of research in theoretical physics. Many mathematical aspects of nonlinear systems, both continuous and discrete, are analyzed here with particular emphasis on the domains of inverse-scattering techniques, singularity analysis, the bilinear formalism, chaos in nonlinear oscillators, Lie-algebraic and group-theoretical methods, classical and quantum integrability, bihamiltonian structures. The book will be of considerable interest to those who wish to study integrable systems, and to follow the future developments, both in mathematics and in theoretical physics, of the theory of integrability.

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Table of contents :
Introduction….Pages 1-4
Nonlinear waves, solitons and IST….Pages 5-29
Integrability — and how to detect it….Pages 30-94
Introduction to the Hirota bilinear method….Pages 95-103
Lie bialgebras, poisson Lie groups and dressing transformations….Pages 104-170
Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property….Pages 171-205
Bifurcations, chaos, controlling and synchronization of certain nonlinear oscillators….Pages 206-255
Eight lectures on integrable systems….Pages 256-296
Bilinear formalism in solition theory….Pages 297-313
Quantum and classical integrable systems….Pages 314-377