A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974

This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

The Inverse Scattering Transformation and The Theory of Solitons

With contributions by numerous experts

This textbook is an introduction to the theory of solitons in the physical sciences.