Some properties of nonlinear wave systems

Nonlinear wave phenomena remain poorly understood, and significant results are limited to either very special examples or situations for which perturbation methods are adequate. The former case is typified by exactly solvable equations and the important role played by solitons. For the latter class of problems, the evolution of weak interactions, resonances, and slowly varying wave trains are well-known examples. Despite the limitations of each approach, these studies have stimulated a large volume of mathematical research and considerable interest in the applied disciplines. One objective of the present paper is to report on some results for nonlinear wave systems that do not fall into either of the above categories. The appro'ach taken is to study a particular case in some detail and, on the basis of the results obtained, to speculate on some anticipated general characteristics of nonlinear