Research On The Exact Solutions Of Three Nonlinear Schr(?)dinger Equations

It is well known that nonlinear partial differential equations are also called evolution equations,which have been widely used to describe the laws of materail change in many fields such as astronomy,physics,life sciences,economic and other fields.Moreover,nonlinear partial differential equations aslo have extensive application prospect.So,it is im-portant to constract exact solutions for nonlinear partial differential equations.In this paper,three nonlinear Schr(?)dinger equations have been studied by three methods.The main objects,methods and results are shown as follows:1.The(G'/G2)expanding method is employed to construct new exact solutions of the variable coefficient Schr(?)dinger equation,and a series of traveling wave solutions with param-eters are obtained,including rational function solutions,trigonometric function solutions and hyperbolic function solutions.When the parameters of the function take special values,kink wave solutions,periodic wave solutions,and solitary wave solutions are further obtained.2.The theory of bifurcations for dynamical system is employed to construct new exact solutions of the generalized nonlinear Schr(?)dinger equation,and a series of solutions are con-structed,which consist of trigonometric function solution,hyperbolic function solutions,Jacobi elliptic function solutions,solitary wave solutions,periodic wave solutions,twisted wave solu-tions,blasting wave solutions.3.The symbolic operations method is employed to construct new exact solutions of the Schr(?)dinger-Hirota equation,and a series of exact solutions are fund,including bell-shaped soliton solutions,trigonometric function solutions,rational function solutions,twisted wave solutions,and Jacobi elliptic function solutions.