中文摘要：

基于其多辛方程组的形式,对满足周期边界条件的KdV方程,在空间方向用Fourier拟谱方法、时间方向用中点隐式辛格式进行离散,得到了KdV方程的多辛Fourier拟谱格式及其相应的守恒律.对不同的孤立波解进行数值模拟,结果验证了所构造格式的有效性与长期数值稳定性.

英文摘要：

The KdV equation with periodic boundary condition was considered in this paper.Based on its multi-symplectic formulation,a multi-symplectic Fourier pseudospectral scheme for the KdV equation was constructed by using Fourier pseudospectral method in space direction and midpoint implicit symplectic scheme in time direction.Its discrete multi-symplectic conservation law was also obtained.The simulation of different solitons showed that the scheme constructed in this paper was effective and had excellent long time numerical behavior.