The Direct Perturbation Method And Approximate Solutions Of Nonlinear Schr(?)dinger Equation Hierarchy

Soliton theory is one of the important branches of nonlinear science. It has crescent application in many fields. And perturbation theory is one of the important parts of soliton theory. So the study of perturbation theory has been increasingly received extensive attention of many researchers. So far, many effective perturbation methods have been established, they can be roughly divided into two kinds. One is the inverse scattering perturbation method, which has important academic value. But this technique is inconvenient to those who are not familiar with the inverse scattering transformation (IST). The other is the direct perturbation method where the squared Jost solutions are employed as the basis for perturbation expansion after soliton equations have been linearized. The method can not completely get rid of the IST because that the squared Jost appear as the particular solution in the process of the IST. The most important technique in this approach is to find eigenfunctions of a linearized operator associated with the linearized equation. However, the eigenfunctions are actually derived...