长水波近似方程组的动力学行为和辛几何算法  

Dynamical Behaviors and Multi-symplectic Preissmann Methods of the Approximate Equations for Long Water Waves

作　　者：王俊杰[1,2] 王连堂[2] 

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

出　　处：《数学的实践与认识》2016年第12期220-229,共10页Mathematics in Practice and Theory

基　　金：云南省教育厅科学研究基金项目(2015y490);普洱学院创新团队(CXTD003)

摘　　要：长水波近似方程组作为一类重要的非线性方程有着许多广泛的应用前景,特别是在浅水非线性色散波的研究中具有重要意义.给出了长水波近似方程组的动力学行为,并基于Hamilton空间体系的多辛理论研究了长水波近似方程组的数值解法,讨论了利用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,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.The approximate equations for long water waves equations, a typical nonlinear wave equations, have many wide application, especially in research of nonlinear dispersion shallow water wave. In the paper, the approximate equations for long water waves equations was sdudied based on the multi-symplectic theory in Hamilton space. The multi-symplectic formulations of the approximate equations for long water waves equations with several conservation laws are presented. The symplectie Preissmann method is used to discretize the formulations. The numerical experiment of the solitary wave is given, and the results verify the efficiency of the multi-symplectic scheme.

关 键 词：长水波近似方程组 Preissmann方法 多辛守恒律 动力学行为 

分 类 号：O175[理学—数学]