中文摘要：

1引言 自冯康院士首次由辛几何的观点提出计算Hamilton系统的辛几何算法后，Bridges和Reich又引入了一个基于某个守恒型偏微分方程多辛结构的多辛积分的概念．对物理学中具有广泛应用的广义高阶非线性Schrodinger方程的保辛算法已有大量的研究工作，但多辛分裂算法还很少，因此对此类算法的研究具有重要的意义．

英文摘要：

A Multi-symplectic Fourier pseudo-spectral scheme for the fourth- order Schrodinger equation with cubic nonlinear term is constructed. We prove that the scheme satisfies full-discrete multi-symplectic conservation laws and charge conservation laws. Then, a split-step multi-symplectic pseudo-spectral scheme is proposed by using the time splitting method. Numerical experiments show that the two schemes constructed in this paper are effective and practicable, and the split-step multi-symplectic pseudo-spectral scheme is significantly better than the multi-symplectic Fourier pseudo-spectral scheme in preserving the charge conservation laws of the original equation and consuming CPU time