一类广义Camassa-Holm方程的多辛Preissmann格式  

MULTI-SYMPLECTIC PREISSMANN METHODS FOR A CLASS OF GENERALIZED CAMASSA-HOLM EQUATIONS

作　　者：王俊杰[1] 王连堂[2] 

机构地区：[1]普洱学院数学系,普洱665000 [2]西北大学数学系,西安710127

出　　处：《系统科学与数学》2013年第11期1321-1331,共11页Journal of Systems Science and Mathematical Sciences

基　　金：云南省教育厅科学研究基金项目(2013Y106)资助课题

摘　　要：Camassa-Holm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,验证了广义Camassa-Holm方程具有Hamilton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广义Camassa-Holm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.Camassa-Holm equation, a typical nonlinear wave equation, has broad application prospect. With the canonical momenta, the new multi-symplectic formulation for the generalized Camassa-Holm equation is presented, and the associatedlocal conservation laws are shown. The generalized Camassa-Holm equation is studied based on the multi-symplectic theory in Hamilton space. The multi-symplectic formulations of the generalized Camassa-Holm equation with several conservation laws are presented. The symplectic Preissmann method is used to discretize the formulations. The numerical example is given, and the results verify the efficiency of the multi-symplectic scheme.

关 键 词：Hamiton系统 PREISSMANN格式 多辛算法 广义CAMASSA-HOLM方程 

分 类 号：O241.82[理学—计算数学]