1. See, for instance, the review paper byA. C. Scott, F. Y. F. Chu andD. W. McLaughlin:Proc. IEEE,61, 1443 (1973).
2. The extensive literature on the theory of the RLW equation can be traced from the references given in the papers on its numerical analysis referenced below. For a (critical) comparison of the RLW to the KdV equation see the paper byM. D. Kruskal in the book edited byJ. Moser:Dynamical Systems, Theory and Applications (Berlin, 1976).
3. Here of course the subscripted variables indicated partial differentiation.
4. In this paper we carefully use the termsoliton only for those solitary waves that appear in the context of KdV-like equations and that have, therefore, among other properties, that of interacting purely elastically. We use instead the termsolitary wave for any solution that travels with constant shape. This nomenclature follows the current practice; it has unfortunately some semantic stridency when discussing theinteraction ofsolitary waves. We hope no reader will be confused.
5. J. C. Eilbeck andM. G. McGuire:Journ. Compt. Phys.,19, 43 (1975);J. C. Eilbeck, J. D. Gibbon andG. R. McGuire:Synergetic study of the regularized long-wave equation, inComputational Methods in Classical and Quantum Physics, edited byM. B. Hooper, Department of Natural Philosophy University of Strathclyde (Glasgow, 1976), p. 378;J. C. Eilbeck andG. R. McGuire:Journ. Compt. Phys.,23, 63 (1977).