Solution Construction Of The Coupled High-order Nonlinear Schr?dinger Equation

In recent years,optical signal processing react fast to time in long distance communication.So,many people concern it.In the early 70’s,people have begun to study the optical soliton.Due to its extraordinary stability,solitons can propagate without attenuation for long distances.It has been occupying a unique position in the study of nonlinear optics.At the same time,it is recognized as the all optical carrier communication system of next generation.In the study of optical solitons,we propose an improved nonlinear Schr?dinger equation model,which is a coupled High-order nonlinear Schrodinger equation.It can describe the ultrashort optical pulse dynamics of the system including two or more interacting light fields.Based on the symbolic computation system-Maple,The exact solutions of the coupled high-order nonlinear Schr?dinger equation were obtained by the Darboux transformation and Lie Symmetry methods.The thesis is arranged as follows:Chapter 1.Introduction,describes the background knowledge of the subject,research significance,and research status at home and abroad.Chapter 2.This chapter introduces the subject to be studied,describes the source of coupled higher-order nonlinear Schr?dinger equation,the main research contents and research methods.Chapter 3.This chapter based on the spectral problem,the Darboux transformation of the equations was obtained.Then,some exact solutions were derived by selecting the trivial solution of the Schr?dinger equation,and pictures were drawn to describe these solutions.Chapter 4.In this chapter,the infinitesimal generator of the equations was obtained by Lie symmetry method.More new solutions of this equation were obtained by solving the initial value problems of first order ordinary differential equations.Chapter 5.Conclusion and prospect.