中文摘要：

基于Hamilton空间体系下的多辛理论,提出组合KdV-mKdV方程的一个多辛方程组.通过离散此方程组,得到原方程的一个多辛Fourier拟谱格式,以及格式的全离散多辛守恒律.由数值结果可知,多辛Fourier拟谱格式能很好地模拟孤立波运动的波形,不出现振荡现象,且在空间方向具有较高的精度和收敛阶.

英文摘要：

Based on the multi-symplectic theory in Hamilton space,a multi-symplectic systems for the combined KdV-mKdV equation is proposed.By discreting the systems,a multi-symplectic Fourier pseudo-spectral scheme is obtained.We also obtain the full-discrete multi-symplectic conservation laws for the scheme.Numerical experiments show that the multi-symplectic Fourier pseudo-spectral scheme can well simulate the motion of the soliton,and does not appear oscillation phenomena with high accuracy and convergence order in space direction.