Introduction to Multidimensional Integrable Equations

The Inverse Spectral Transform in 2+1 Dimensions

  • B. G. Konopelchenko
  • C. Rogers

Part of the Plenum Monographs in Nonlinear Physics book series (PMNP)

Table of contents

  1. Front Matter
    Pages i-x
  2. B. G. Konopelchenko
    Pages 1-45
  3. B. G. Konopelchenko
    Pages 203-236
  4. B. G. Konopelchenko
    Pages 237-238
  5. Back Matter
    Pages 239-292

About this book

Introduction

The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis­ covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans­ form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.

Keywords

Soliton integrable system solution spectra

Authors and affiliations

  • B. G. Konopelchenko
    • 1
  1. 1.Institute of Nuclear PhysicsNovosibirskRussia

Editors and affiliations

  • C. Rogers
    • 1
  1. 1.Loughborough University of TechnologyLeicestershireEngland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4899-1170-4
  • Copyright Information Springer-Verlag US 1992
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-1172-8
  • Online ISBN 978-1-4899-1170-4
  • About this book