摘要
二阶KdV类型水波方程作为一类重要的非线性方程有着许多广泛的应用前景.通过引入正则动量,验证了二阶KdV类型的水波方程具有两种Hamilton系统多辛格式,并证实此格式具有多辛守恒律、局部能量守恒律和动量守恒律.基于Hamilton空间体系的多辛理论研究了二阶KdV类型水波方程的数值解法,利用中心Preissmann方法构造离散多辛格式的途径,并构造了一种典型的半隐式的多辛格式,该格式满足多辛守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性.
A two order wave equation of kdv type, a typical nonlinear wave equation, has broad application prospect. With the canonical momenta, two new multi-symplectic formulations for the two order wave equation of KdV type are presented, and the associated local conservation laws are shown. A two order wave equation of kdv type was sdudied based on the multi-symplectic theory in Hamilton space.The multi-symplectic formulations of a two order wave equation of kdv type with several conservation laws are presented. The symplectic Preissmann method is used to discretize the formulations. The numerical experiment is given, and the results verify the efficiency of the multi-symplectic scheme.
出处
《应用数学学报》
CSCD
北大核心
2014年第3期393-406,共14页
Acta Mathematicae Applicatae Sinica
基金
云南省教育厅基金(2013Y106)资助项目
