Toward the Multisoliton Perturbation Theory

Abstract

The one-soliton perturbation theory was formulated several years ago by Kaup /I/, Kaup and Newel1 / Z / , and Karpman and Maslov / 3 / . It was constructed on the basis of the inverse scattering method (ISM) and developed for a few main soliton systems like the Korteweg-de Vries (KdV) , sine-Gordon (SG) , o r the nonlinear Schrodinger equation (NSE). Unfortunately, up to now there exists no effective extension of this theory onto the multisoliton case. The reason is that in direct application of the ISM approach to such a case one is confronted with significant technical difficulties, and simplifying approximations are necessary / 4 , 5 / .Moreover) because of these difficulties, there are some soliton systems) like the Benjamin-Ono equation, the Sawada-Kotera equation and others, for which even one-soliton perturbation theory is unknown.In this note we report a new approach to the multisoliton perturbation theory which overpasses the difficulties mentioned above, at least in the frame of the so-