The Exact Solutions Of NLSE With Derivative Non-Kerr Terms And Higher Order Dispersive Cubic-Quintic NLSE

The nonlinear partial differential equation is an important branch of mathe-matics.In real life,it is an important model for describing the problems of non-linear phenomenon,such as hydrodynamics,plasma physics,photobiology,solid physics,atmospheric phenomena,engineering and medicine.When we want to understand the principles of these physical phenomena,we must accurately solve the exact solutions of nonlinear partial differential equations.Then we study the properties described by the nonlinear partial differential equations.Therefore,it is extremely important to find the exact solutions of nonlinear partial differen-tial equations.Many methods have been used to solve the solutions of nonlinear partial differential equations.However,there are still many nonlinear partial dif-ferential equations with important physical significance whose exact solutions have not been obtained.Therefore,Many nonlinear partial differential equations still need further study and analysis,and their solution space needs to be constantly expanded and enrichedIn this thesis,the exact travelling solutions of the high order nonlinear Schrodinger equation(NLSE)with derivative Non-Kerr nonlinear terms and the higher order dispersive Cubic-Quintic nonlinear Schrodinger equation are obtained by using the first integral method,the special kind(G'/G)-expansion method and the new mapping method.Firstly,we turn them into the ordinary differential equation by proper travelling wave transformation.Secondly,the two high order nonlinear Schrodinger equations are solved by using these methods and applying Maple software in detail which the exact solutions of the two equations are ob-tained.Finally,the applicable forms of three methods are given.And the same time,the exact solutions obtained in this thesis are compared with those obtained by different methods.It shows that the exact solutions obtained in this thesis are both generalized and extendedIn this work,the exact solutions including the periodic wave solution,the solitary wave solution,bright and dark soliton solution and the singular soliton solution are obtained.They are represented by exponential functions,trigonomet-ric functions and hyperbolic functions.From the solving process and results,the first integral method,the special kind(G'/G)-expansion method and the new map-ping method have the characteristics of simplicity,directness and effectiveness about solving the exact travelling wave solutions of nonlinear partial differential equations.In other words,Tedious calculations can be avoided by Maple software,the solutions of more accurate and richer travelling wave solutions are obtained.Therefore,these methods can be extended to solve nonlinear partial differential equations of multiple systems.