SRLW方程的多辛中点格式

Multi-symplectic Algorithm of SRLW Equation

考虑对称正则长波(SRLW)方程的多辛算法.辛算法是从辛几何观点出发,利用变分原理构造的具有保持原Ham-ilton系统辛几何结构性质的一种算法.本文利用正则变换,构造正则长波方程的多辛方程组,利用多辛算法离散此多辛方程组,得到一个多辛中点格式,要求所得到的多辛格式满足离散形式的多辛守恒律,并分析了它的线性部分的稳定性.用数值实验验证了所构造的格式具有长时间的数值稳定性,它们还能很好地模拟原孤立波的波形.

Some multi-symplecitc schemes for SRLW equation were considered in the paper. Symplectic algorithms set forth sympleetic geometry, It makes use of variation principal and it requests that schemes should maintain symplectic geometric traits of the original Hamiltonian system. Multi-sympleetie equation for SRLW PDES through canonical transformations was constructed. Muhisymplectic equations with muhi-symplectic schemes which must preserve discrete multi-sympleetie conservation law was disereted. A multi-symplectic midpoint scheme for SRLW equation was obtained, Experiments showed that muhi-sympleetic scheme had long time behavior and could preserving original solitary wave shape well.