Title

A Heuristic Guide to Nonlinear Dispersive Wave Equations and Soliton-Type Solutions

Document Type

Article

Publication Date

9-1984

Publication Source

Proceedings of the IEEE

Abstract

In this paper we present a heuristic way of constructing nonlinear dispersive equations that lead to soliton or soliton-type solutions. We assume only that a general knowledge of the dispersion relation of the system is known, together with some insight into the effect of nonlinearity on wave speed. We show that such knowledge is sufficient to derive most known soliton equations and thus to provide the engineer with a quick way to assess whether or not his particular system is likely to exhibit soliton behavior. Naturally, a more detailed description requires knowledge of the basic equations governing the system and special techniques to handle initial conditions. To that purpose we provide the reader with ample references which he may want to consult in order to augment the information gained by the method outlined in this paper.

Inclusive pages

1109-1130

ISBN/ISSN

0018-9219

Comments

Permission documentation is on file.

Publisher

IEEE

Volume

72

Issue

9

Peer Reviewed

yes