Exact Solution Of Isospectral Or Non-isospectral General Nonlinear Schr?dinger Equation With Derivative

In this paper,we study the exact solution of the isospectral or non-isospectral General Nonlinear Schr?dinger Equation with Derivative.The major contents include contain the N-soliton solutions of the non-isospectral General Nonlinear Schr?dinger Equation with Derivative are obtained through the Hirota method,and give the dynamical characteristics of the solution.This equation and its solution can reduce to the non-isospectral Nonlinear Schr?dinger Equation with Derivative and its solution.The general double Wronskian Solutions,soliton solutions and rational solutions of the General Nonlinear Schr?dinger Equation with Derivative are gained through the Wronskian techniqueand.In the first chapter,we mainly review the generation and development of soliton theory,and introduce the common solving methods of soliton equations.In the second chapter,we briefly describe some basic concepts and important properties of bilinear derivatives and Wronskian determinants.In the third chapter,based on the Kaup-Newell spectral problem,we derived the non-isospectral General Nonlinear Schr?dinger Equation.The equation obtained one-,two-,N-soliton solutions under the appropriate conditions using the Hirota method.Meanwhile,the dynamical characteristics of one-soliton solutions and two-soliton interactions are given,and the soliton solutions of the non-isospectral Nonlinear Schr?dinger Equation with Derivative in the form of Hirota are given by reduction.In the fourth chapter,on the basis of Wronskian technique,the condition of satisfying the double Wronskian elements is extended to the matrix form,and the generalized double Wronskian solution of the equation is given,furthermore,soliton solutions and rational solutions are obtained.In the fifth chapter,we summarizes the thesis and expect the future work.