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Integrable Hamiltonian Hierarchies

Spectral and Geometric Methods

  • V.S. Gerdjikov
  • G. Vilasi
  • A.B. Yanovski

Part of the Lecture Notes in Physics book series (LNP, volume 748)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Integrable Hamiltonian Hierarchies: Spectral Methods

    1. Front Matter
      Pages 1-1
    2. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 3-36
    3. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 37-70
    4. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 71-95
    5. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 97-132
    6. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 133-173
    7. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 175-209
    8. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 211-245
    9. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 247-314
    10. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 315-354
  3. Integrable Hamiltonian Hierarchies: Geometric Theory of the Recursion Operators

    1. Front Matter
      Pages 355-355
    2. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 357-371
    3. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 373-406
    4. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 407-458
    5. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 459-471
    6. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 473-513
    7. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 515-545
    8. V.S. Gerdjikov, G. Vilasi, A.B. Yanovski
      Pages 547-611
  4. Back Matter
    Pages 613-643

About this book

Introduction

This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform.

The book brings together the spectral and the geometric approaches and as such
will be useful to a wide readership: from researchers in the field of nonlinear
completely integrable evolution equations to graduate and post-graduate students.

Keywords

Fourier transform Hierarchies of Hamiltonian Equations Recursion Operators direct scattering problem inverse scattering problem

Editors and affiliations

  • V.S. Gerdjikov
    • 1
  • G. Vilasi
    • 2
  • A.B. Yanovski
    • 3
  1. 1.Bulgarian Academy of SciencesInst. Nuclear Research & Nuclear EnergyGermany
  2. 2.Dipto. Fisica Ist. Nazionale di Fisica NucleareUniversità SalernoItaly
  3. 3.Dept. Mathematics & Applied MathematicsUniversity of Cape Town7701 South Africa

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-77054-1
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-77053-4
  • Online ISBN 978-3-540-77054-1
  • Series Print ISSN 0075-8450
  • Buy this book on publisher's site