Korteweg-de Vries方程的MSPRK方法

摘要

@@ We consider the Korteweg-de Vries (KdV) equation in the formrnut + uux + uxxx = 0, (1)rnwhich is a nonlinear hyperbolic equation and has smooth solutions for all the time. There are a vast of results can be found in the literature for this equation, both theoretical and numerical. However, several good reasons account for needs of another numerical study of this equation are listed in [1]. Among them, the most convincing one might be that the wave equations have the multi-symplectic structure (cf. [2]), and the KdV equation is therefore a natural test bed for the study of the multi-symplectic integration, namely, numerical scheme that can preserve the multi-symplectic structure which thus endows the simulations with more physics.