非线性Schrdinger方程的显式模守恒格式

Explicit Modulus Conserving Scheme for the Nonlinear Schrdinger Equation

本文采用Magnus方法求解非线性Schrdinger方程。Schrdinger方程具有模平方守恒特性,用适当差分格式对其进行模平方守恒空间离散,转化成模平方守恒的常微分方程组,再用Magnus方法求解。数值结果表明Magnus方法能保非线性Schrdinger方程模守恒量的优越性和好的稳定性。Magnus方法可应用到其它模守恒的微分方程。

This paper applies apply the Magnus method to solve the nonlinear SchrSdinger equation. The nonlinear Schrodinger equation has the modulus conserving property. The nonlinear SchrSdinger equation is discretizated in the spacial direction by the proper difference scheme, which is transformed into the ordinary differential equations. The ordinary differential equations are solved by the Magnus method. Numerical results show that the Magnus method have the advantage of the modulus conserving property of the nonlinear SchrSdinger equation and its good stability. The Magnus method can be applied to other modulus conserving differential equations.