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Hamiltonian Methods in the Theory of Solitons

  • Ludwig D. Faddeev
  • Leon A. Takhtajan

Part of the Springer Series in Soviet Mathematics book series (CLASSICS)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Introduction

    1. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 1-8
  3. The Nonlinear Schrödinger Equation (NS Model)

    1. Front Matter
      Pages 9-9
    2. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 11-80
    3. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 81-185
    4. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 186-278
  4. General Theory of Integrable Evolution Equations

    1. Front Matter
      Pages 279-279
    2. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 281-355
    3. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 356-470
    4. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 471-522
    5. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 523-576
  5. Conclusion

    1. Ludwig D. Faddeev, Leon A. Takhtajan
      Pages 577-577
  6. Back Matter
    Pages 579-594

About this book

Introduction

The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation, rather than the (more usual) KdV equation, is considered as a main example. The investigation of this equation forms the first part of the book. The second part is devoted to such fundamental models as the sine-Gordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions.

Keywords

Inverse scattering method Lie-Algebra Riemann problem Schrödinger equations curvature integrable Evolution Equations soliton

Authors and affiliations

  • Ludwig D. Faddeev
    • 1
  • Leon A. Takhtajan
    • 1
  1. 1.Steklov Mathematical InstituteLeningradUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-69969-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-69843-2
  • Online ISBN 978-3-540-69969-9
  • Series Print ISSN 1431-0821
  • Buy this book on publisher's site
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