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Important Developments in Soliton Theory

  • Book
  • © 1993

Overview

Editors:
  1. A. S. Fokas

    1. Clarkson University, Potsdam, USA

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  2. V. E. Zakharov

    1. Landau Institute for Theoretical Physics, Moscow, Russia
      University of Arizona, Tucson, USA

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    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (25 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    1. Introduction

      • A. S. Fokas, V. E. Zakharov
      Pages 1-4

  3. Methods of Solution

    1. Front Matter

      Pages 5-5
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    2. The Inverse Scattering Transform on the Line

      • R. Beals, P. Deift, X. Zhou
      Pages 7-32

    3. C-Integrable Nonlinear Partial Differential Equations

      • F. Calogero
      Pages 33-37

    4. Integrable Lattice Equations

      • H. W. Capel, F. Nijhoff
      Pages 38-57

    5. The Inverse Spectral Method on the Plane

      • R. Coifman, A. S. Fokas
      Pages 58-85

    6. Dispersion Relations for Nonlinear Waves and the Schottky Problem

      • B. Dubrovin
      Pages 86-98

    7. The Isomonodromy Method and the Painlevé Equations

      • A. S. Fokas, A. R. Its
      Pages 99-122

    8. The Cauchy Problem for Doubly Periodic Solutions of KP-II Equation

      • I. Krichever
      Pages 123-146

    9. Integrable Singular Integral Evolution Equations

      • P. M. Santini
      Pages 147-177

  4. Asymptotic Results

    1. Front Matter

      Pages 179-179
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    2. Long-Time Asymptotics for Integrable Nonlinear Wave Equations

      • P. A. Deift, A. R. Its, X. Zhou
      Pages 181-204

    3. The Generation and Propagation of Oscillations in Dispersive Initial Value Problems and Their Limiting Behavior

      • P. D. Lax, C. D. Levermore, S. Venakides
      Pages 205-241

    4. Differential Geometry and Hydrodynamics of Soliton Lattices

      • S. P. Novikov
      Pages 242-256

  5. Algebraic Aspects

    1. Front Matter

      Pages 257-257
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    2. Bi-Hamiltonian Structures and Integrability

      • A. S. Fokas, I. M. Gel’fand
      Pages 259-282

    3. On the Symmetries of Integrable Systems

      • P. G. Grinevich, A. Yu. Orlov, E. I. Schulman
      Pages 283-301

    4. The n-Component KP Hierarchy and Representation Theory

      • V. G. Kac, J. W. van de Leur
      Pages 302-343

    5. Compatible Brackets in Hamiltonian Mechanics

      • H. P. McKean
      Pages 344-354
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Keywords

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.

Editors and Affiliations

  • Clarkson University, Potsdam, USA

    A. S. Fokas

  • Landau Institute for Theoretical Physics, Moscow, Russia

    V. E. Zakharov

  • University of Arizona, Tucson, USA

    V. E. Zakharov

Bibliographic Information

  • Book Title: Important Developments in Soliton Theory

  • Editors: A. S. Fokas, V. E. Zakharov

  • Series Title: Springer Series in Nonlinear Dynamics

  • DOI: https://doi.org/10.1007/978-3-642-58045-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Hardcover ISBN: 978-3-540-55913-9Published: 23 September 1993

  • Softcover ISBN: 978-3-642-63450-5Published: 23 October 2012

  • eBook ISBN: 978-3-642-58045-1Published: 06 December 2012

  • Series ISSN: 0940-2535

  • Edition Number: 1

  • Number of Pages: IX, 559

  • Topics: Complex Systems, Analysis, Statistical Physics and Dynamical Systems

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