Important Developments in Soliton Theory

  • A. S. Fokas
  • V. E. Zakharov

Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Introduction

    1. A. S. Fokas, V. E. Zakharov
      Pages 1-4
  3. Methods of Solution

    1. Front Matter
      Pages 5-5
    2. R. Beals, P. Deift, X. Zhou
      Pages 7-32
    3. H. W. Capel, F. Nijhoff
      Pages 38-57
    4. R. Coifman, A. S. Fokas
      Pages 58-85
    5. A. S. Fokas, A. R. Its
      Pages 99-122
  4. Asymptotic Results

    1. Front Matter
      Pages 179-179
    2. P. A. Deift, A. R. Its, X. Zhou
      Pages 181-204
  5. Algebraic Aspects

    1. Front Matter
      Pages 257-257
    2. A. S. Fokas, I. M. Gel’fand
      Pages 259-282
    3. P. G. Grinevich, A. Yu. Orlov, E. I. Schulman
      Pages 283-301
    4. V. G. Kac, J. W. van de Leur
      Pages 302-343
    5. A. B. Shabat, A. V. Mikhailov
      Pages 355-374
    6. V. Zakharov, A. Balk, E. Schulman
      Pages 375-404
  6. Quantum and Statistical Mechanical Models

    1. Front Matter
      Pages 405-405
    2. A. R. Its, A. G. Izergin, V. E. Korepin, N. A. Slavnov
      Pages 407-417
    3. L. A. Takhtajan
      Pages 441-467
    4. M. Wadati
      Pages 468-486
  7. Near-Integrable Models and Computational Aspects

    1. Front Matter
      Pages 487-487
    2. M. J. Ablowitz, B. M. Herbst
      Pages 489-510
    3. P. Deift, L.-C. Li, C. Tomei
      Pages 511-536
    4. D. W. McLaughlin
      Pages 537-558
  8. Back Matter
    Pages 559-559

About this book


In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.


Eigenvalue Hamiltonian mechanics Mathematische Physik Nichtlineare Dynamik Solitonen algebraic geometry development differential equation gravity integrable system integral mathematical physics nonlinear dynamics partial differential equation solitions

Editors and affiliations

  • A. S. Fokas
    • 1
  • V. E. Zakharov
    • 2
    • 3
  1. 1.Clarkson UniversityPotsdamUSA
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia
  3. 3.University of ArizonaTucsonUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63450-5
  • Online ISBN 978-3-642-58045-1
  • Series Print ISSN 0940-2535
  • Buy this book on publisher's site