二阶等谱AKNS系统的多种守恒律及多辛格式  

Applying Theory of Bridges et al to Second-Order Isospectral AKNS Equations

作　　者：韩松梅[1] 胡伟鹏[1] 邓子辰[1,2] 张劲夫[1] 

机构地区：[1]西北工业大学力学与土木建筑学院,陕西西安710072 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116023

出　　处：《西北工业大学学报》2010年第4期525-529,共5页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(10972182;10772147和10632030);111引智计划(B07050);西北工业大学基础研究基金(JC200938);中国博士后科学基金(20090450170);大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802)资助

摘　　要：在Hamilton体系下,Bridges等人将针对有限维系统的辛算法推广到应用于无限维系统的多辛算法,为开展复杂非线性问题的保结构算法研究奠定了数学基础。文章通过引入正交动量,构造二阶等谱AKNS方程组的一阶多辛偏微分方程组形式,推导出了其多种守恒律。随后构造其等价于Preissmann Box格式的半隐式多辛格式对二阶等谱AKNS方程组的单孤子解进行了数值模拟。将数值模拟结果与解析解进行对比,该多辛格式良好的长时间数值稳定性和高精度特点得到了充分验证。Bridges et al in Refs.1 and 2 extended the symplectic algorithm for finite dimensional Hamilton system to the multi-symplectic algorithm for infinite dimensional Hamilton system;this extension is generally acknowledged to play an important role in studying the structure preserving algorithm of a complex nonlinear problem.Applying the extension of Bridges et al to second-order isospectral AKNS equations,section 1 of the full paper,by introducing suitable orthogonal momenta,derives multi-symplectic formulations with several conservation laws according to the Hamilton variational principle.Section 2 deduces a semi-implicit multi-symplectic scheme,which is equivalent to the Preissmann Box scheme.Section 3 derives the single-soliton of the second-order isospectral AKNS equations;q and r can be computed with eq.（21）.Numerical simulation results are given in Figs.1,2 and 3 and Table 1.These results show preliminarily that the multi-symplectic scheme is very good in two respects：（1） high precision;（2） long-time stable numerical behaviour and good conservation.

关 键 词：多辛 等谱AKNS方程组 孤子解 

分 类 号：O175.29[理学—数学]