第一类导数非线性薛定谔方程的数值模拟

Numerical simulation for the first type derivative nonlinear Schrdinger equation

利用Taylor级数展开,给出了求解第一类导数非线性薛定谔方程的CrankNicolson格式。使用该格式对该方程进行数值模拟,数值算例验证了该格式具有保持时空2阶精度的性质。最后在初值上添加微小随机扰动,观察孤子解随时间的变化情况,结果显示孤子解在初值添加微小随机扰动后变化不大,说明孤子解具有很好的稳定性。

The Crank-Nicolson scheme for the first type derivative nonlinear Schrdinger equation is given by using the Taylor series expansion method. Then the equation is solved by using the CrankNicolson scheme and the numerical experiments verify that the Crank-Nicolson scheme has the property of keeping second order accuracy in time and space. In the end,the behavior of soliton solution is observed by adding a small perturbation to the initial value. As a result,the soliton solution changes little when small perturbation is added to the initial value,which proves high stability of soliton solution.