Algebraic Methods in Nonlinear Perturbation Theory

  • V. N. Bogaevski
  • A. Povzner

Part of the Applied Mathematical Sciences book series (AMS, volume 88)

Table of contents

  1. Front Matter
    Pages i-xii
  2. V. N. Bogaevski, A. Povzner
    Pages 1-15
  3. V. N. Bogaevski, A. Povzner
    Pages 47-126
  4. V. N. Bogaevski, A. Povzner
    Pages 127-193
  5. V. N. Bogaevski, A. Povzner
    Pages 195-258
  6. Back Matter
    Pages 259-266

About this book

Introduction

Many books have already been written about the perturbation theory of differential equations with a small parameter. Therefore, we would like to give some reasons why the reader should bother with still another book on this topic. Speaking for the present only about ordinary differential equations and their applications, we notice that methods of solutions are so numerous and diverse that this part of applied mathematics appears as an aggregate of poorly connected methods. The majority of these methods require some previous guessing of a structure of the desired asymptotics. The Poincare method of normal forms and the Bogolyubov-Krylov­ Mitropolsky averaging methods, well known in the literature, should be mentioned specifically in connection with what will follow. These methods do not assume an immediate search for solutions in some special form, but make use of changes of variables close to the identity transformation which bring the initial system to a certain normal form. Applicability of these methods is restricted by special forms of the initial systems.

Keywords

algebra applied mathematics bifurcation differential equation eigenvalue electromagnetic field field manifold matrix ordinary differential equation transformation

Authors and affiliations

  • V. N. Bogaevski
  • A. Povzner
    • 1
  1. 1.Institute of the Physics of the EarthAcademy of Science—USSRMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4438-7
  • Copyright Information Springer-Verlag New York 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8770-4
  • Online ISBN 978-1-4612-4438-7
  • Series Print ISSN 0066-5452
  • About this book
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