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Integrability of Nonlinear Systems

  • Conference proceedings
  • © 1997

Overview

Editors:
  1. Y. Kosmann-Schwarzbach
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  2. B. Grammaticos
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  3. K. M. Tamizhmani
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Part of the book series: Lecture Notes in Physics (LNP, volume 495)

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Table of contents (10 papers)

  1. Front Matter

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  2. Introduction

    Pages 1-4

  3. Nonlinear waves, solitons and IST

    • M. J. Ablowitz
    Pages 5-29

  4. Integrability — and how to detect it

    • B. Grammaticos, A. Ramani
    Pages 30-94

  5. Introduction to the Hirota bilinear method

    • J. Hietarinta
    Pages 95-103

  6. Lie bialgebras, poisson Lie groups and dressing transformations

    • Y. Kosmann-Schwarzbach
    Pages 104-170

  7. Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property

    • M. D. Kruskal, N. Joshi, R. Halburd
    Pages 171-205

  8. Bifurcations, chaos, controlling and synchronization of certain nonlinear oscillators

    • M. Lakshmanan
    Pages 206-255

  9. Eight lectures on integrable systems

    • F. Magri, P. Casati, G. Falqui, M. Pedroni
    Pages 256-296

  10. Bilinear formalism in solition theory

    • J. Satsuma
    Pages 297-313

  11. Quantum and classical integrable systems

    • M. A. Semenov-Tian-Shansky
    Pages 314-377

  12. Back Matter

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Keywords

About this book

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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