Study On Traveling Wave Solutions And Stability Of Several Nonlinear Development Equations

In this paper,several kinds of nonlinear development equations are studied by using auxiliary functions and various methods to solve nonlinear development equations.On the basis of GSS orbital stability theory,the orbital stability and instability of soliton solutions of a class of generalized composite KdV equations are studied by using fine mathematical analysis method.Main content of the paper:Chapter 1 Introduction.The nonlinear differential equations,soliton and the orbital stability of the solutions are simply illustrated.Several methods to study the solutions of nonlinear development equations are briefly introduced.In the end,brief and concise description of the main research content.Chapter 2 This chapter briefly introduces the methods used in this paper and the basic knowledge of the theory,including(G'/G,1/G)expansion method;Elliptic integral and basic knowledge of orbital stability theory Jacobi elliptic function;Orbital stability theory proposed by Grillakis et al.Chapter 3 A class of optical metamaterial equations is studied in this chapter,and the exact traveling wave solution(soliton)of the equation rational form,triangular form and hyperbolic form is obtained by using the(G'/G,1/G)expansion method combined with Maple---a software of symbolic calculation,and the waveform diagram of its soliton is drawn.Chapter 4 This chapter studies the exact solutions of a class of ultrashort optical soliton transmission equations under corr law and parabolic law.By depicting the planar phase diagram of the parameters of the equation,we obtain different parameter expressions for their exact solutions under different parameter conditions.Chapter 5 A class of nonlinear Schrodinger equations containing Raman solitons is studied in this chapter,and a large number of accurate traveling wave solutions of the nonlinear development equation are obtained by auxiliary equation and constructing solution method.Chapter 6 This chapter studies the orbital stability of soliton of a class of generalized composite KdV equations,expands the results of previous literature on this problem,and proves the orbital stability and instability of their soliton in different parameter ranges.Chapter 7 Summarizes the main research contents of this paper and puts forward the prospect for the future research direction.