孤立波方程的保结构算法  

Structure Preserving Algorithms for Soliton Equations

作　　者：王雨顺[1,2] 王斌[2] 季仲贞[2] 

机构地区：[1]南京师范大学数学与计算机学院 [2]中国科学院大气物理所

出　　处：《计算物理》2004年第5期386-400,共15页Chinese Journal of Computational Physics

基　　金：自然科学基金创新群体(No.40221503);国家基础研究重点发展规划(No.199903208)资助项目

摘　　要：　讨论了孤立波方程的保结构差分算法,以一些经典的孤立波方程为例,如KdV,sine Gordon,K P方程,给出了它们的辛和多辛结构,说明辛和多辛算法的可适用性.提出局部守恒算法和广义保结构算法的概念,它们是保结构算法的概念自然推广.还给出一种能系统构造局部守恒格式的复合方法.数值例子说明,保结构数值能很好模拟各种孤立波的演化.The structure preserving difference algorithms for soliton equations are investigated. The symplectic structures and multisymplectic structures of the classical solitary wave equations such as the KdV, sine-Gordon and KP equations are presented to illustrate the applicability of the symplectic and multisymplectic algorithms. The concept of local conservative schemes and generalized structure preserving algorithms, which are natural generalizations of the structure preserving algorithms, are also proposed. A new concatenating method to systematically construct local conservative schemes and some numerical experiments of the constructed schemes are also presented.

关 键 词：孤立波 守恒 多辛算法 方程 广义 推广 演化 概念 数值 经典 

分 类 号：O241.82[理学—计算数学] G633[理学—数学]