高阶非线性薛定谔方程的离散梯度法

提出了一种新的离散梯度法求解高阶非线性薛定谔方程．首先利用离散梯度法离散高阶非线性薛定谔方程，得到高阶非线性薛定谔方程的离散梯度格式，然后利用高阶非线性薛定谔方程的离散梯度格式和相应的辛格式，在不同饱和非线性效应和不同振辐下对孤立子进行数值模拟．数值结果表明，离散梯度格式能很好地模拟高阶非线性薛定谔方程中孤立子行为，比辛格式更好地保持Hamilton系统的能量．

Dispersed Gradient Method of High Order Nonlinear Schr(o)dinger Equation

In the report, a new dispersed gradient method was proposed for solving the high order nonlinear Schrodinger Equation. Firstly, the dispersed gradient method was used to discrete the high order nonlinear Schrodinger Equation and the dispersed gradient scheme of the high order nonlinear Schrodinger Equation was obtained. Secondly, the discrete gradient scheme and the corresponding symplectic scheme of the high order nonlinear Schrodinger Equation with the different saturated nonlinear effects and the different amplitudes were used to simulate the soliton behaviors. The results indicated that the dispersed gradient scheme can simulate the solitons behaviors of the high order nonlinear Schrodinger equation very well and preserve the energy conservation of the Hamiltonian system better than the symplectic scheme.