With A Weak Disturbance Schr (?) Comparison Of Analytical And Numerical Solutions Of Dinger Equation

In this paper,we mainly discussed the approximate analytic solution of nonlinear Schrodinger equation with tiny disturbance . We got the following rules when we compared the analytic solution with the numeical result which is computed by the method of Runge-Kutta-Nystrom with multi-symplectic.1.The real part and imaginary part of numeical solution and analytic solution possess the same symmetry tendency.2.The error between the numerical solution and the two-order approximate analytic solution is smaller than the error between the numerical solution and the one-order approximate analytic solution.3.When e turns to small,the difference between the two-order approximate analytic solution and the one-order approximate analytic solution becomes small; When becomes small to some degree, there is almost no difference.4.When e turns to small,the difference between numerical solution and analytic solution becomes small; When e becomes small to some degree,the error has no change.5.When turns to small,the range of vibration of real part and imaginary part becomes small; When e becomes small to some degree,the amplitude has no change .This paper is composed of three parts. In the first chapter, we introduce the historical background of the problems which will be investigated and the main frame. In the second chapter, in Section 2.1, we introduce approximate method of which is fundamental for the subsequent developments. In Section 2.2,we compute the one-order approximate analytic solution of nonlinear Schrodinger equation . In Section 2.3,we compute the two-order approximate analytic solution of nonlinear Schrodinger equation. In Section 3.1 we introduce the main numerical method of nonlinear Schrodinger equation. In Section 3.2,we got some main rules when we compared the analytic solution with the numeical result .