The Research Of Solving The Solutions Of The Schr?dinger Equation Of Higher Order Nonlinear Terms And The Properties Of The Solutions

In this paper, by using the relevant conclusions of the B?cklund transformation and the nonlinear superposition formulas of the solutions of Riccati equation and the second kind of elliptic equation and so on auxiliary equations, with the help of symbolic computing system Mathematica, obtains the new infinite sequence solutions of several of the Schr?dinger equation, and analyses the qualitative understanding of solutions.In the first chapter, introduces the discovery of the soliton and soliton theory development. In addition, also introduces the physical background of the Schr?dinger equation and the main work of this article.In the second chapter, by using the solutions of the Riccati equation, B?cklund transform and nonlinear superposition formula,constructs the new infinite sequence solutions of nonlinear LC circuit equations consisting of trigonometric function, hyperbolic function and rational function, and analyses the properties.In the third chapter, firstly, the one-dimensional nonlinear Schr?dinger equation with the fifth power has made a series of transformation, and then obtains a nonlinear ordinary differential equation. Then, by using the relevant conclusions of the B?cklund transformation and the nonlinear superposition formulas of the solutions of Riccati equation, structures the new infinite sequence solutions of one-dimensional nonlinear Schr?dinger equation with fifth power consisting of trigonometric function and hyperbolic function, and analyses the properties.In the fourth chapter, by using the solutions of second kinds ofelliptic equation and the B?cklund transform, obtains the new infinite sequence solutions of(2+1)-dimensional Cubic-Quintic nonlinear Schr?dinger equation consisting of trigonometric function, Riemann theta function and exponential function, and analyses the properties.In the fifth chapter, firstly, the long-short-wave interaction equations are transformed into the first kind of elliptic equation. Then,by using the relevant conclusions of B?cklund transform of first kind of elliptic equations, constructs the new infinite sequence solutions of long-short-wave interaction equations, and analyses the properties of the solutions. These solutions include Jacobi elliptic function solutions, hyperbolic function solutions, exponential function solutions and rational function solutions.