Soliton Perturbation Theory For A Sort Of Nonlinear Evolution Equations

Soliton theory is one of the important branch of nonlinear science. And soliton perturbation theory is one of the important parts of soliton theory. So the study of soliton perturbation theory has been increasingly received extensive attention of many researchers. In this thesis, we study systematically and allsidedly soliton perturbation theory for a sort of nonlinear evolution equations.This thesis consists of four chapters. The chapter one includes mainly following three part contents. Firstly ,we briefly introduce the modern studies and situation of application of soliton theory .Secondly, we concisely recall the formation and development of soliton perturbation theory. And we put emphasis on three kinds of representative soliton perturbation theories, at the same time, we point out some merits and defects of these theories respectively. Thirdly, we briefly recommend the study ofa sort of nonlinear evolution equations:UTT-a1UXX + a3U + a4U3 =0. In chapter two, we use a new direct approach to the study of soliton perturbation of the sort of nonlinear wave equations with a, >0 in detail. In chapter three, we apply the new direct approach to the study of soliton perturbation of the sort nonlinear nonwave equations with a, <0. In chapter four, we give the summary of our research.