Research On The Rogue Wave Solutions Of The Deformable Integrable System

Nonlinear science has important applications in plasma theory,fluid mechanics and nonlinear optics.Deformation integrable system is one of the important research directions of soliton theory which is one of the important branches of Nonlinear Science.Nonlinear equations with self-consistent sources add non-homogeneous terms to the original equation,which can be used to describe the interactions between different waves,so as to explain more basic laws of corresponding natural phenomena.It is a kind of important deformation integrable system.In this paper,we start from the Darboux transformation in soliton and integrable system,the generalized Darboux transformation for the nonlinear Schrodinger equation with the self-consistent sources is constructed.We mainly discuss the rogue wave solution,the breathe solution and their interactions by the generalized Darboux transformation and give the general form of the higher order rogue wave solutions of the nonlinear Schrodinger equation with the self-consistent sources,the dynamic behaviors of the solution are analyzed.Based on it,the class of the nonlinear Schrodinger equation with self-consistent sources is studied and the deformation integrable system of the PT-symmetric nonlinear Schrodinger equation is constructed and its solution is studied.The soliton,the rational soliton and the rogue wave solutions with different properties are obtained by the different parameter values.The forms of degenerated solitons are given and the dynamic behaviors of them are analyzed.This paper presents a general generalized Darboux transformation method to solve the deformation integrable system,which provides a theoretical basis for physical experiments.