Nearly Integrable Infinite-Dimensional Hamiltonian Systems

  • Authors
  • Sergej¬†B.¬†Kuksin

Part of the Lecture Notes in Mathematics book series (LNM, volume 1556)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Sergej B. Kuksin
    Pages 45-90
  3. Back Matter
    Pages 91-101

About this book

Introduction

The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.

Keywords

Hamiltonian System KAM-theory differential equation infinite-dimensional integrable systems partial differential equation quasiperiodic solution

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0092243
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57161-2
  • Online ISBN 978-3-540-47920-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book