Camassa-Holm方程的拟周期解及其渐近行为

王振; 秦玉鹏; 邹丽; 马瑞芳; 朱贵勋

doi:10.3879/j.issn.1000-0887.2015.09.010

Camassa-Holm方程的拟周期解及其渐近行为

doi: 10.3879/j.issn.1000-0887.2015.09.010

¹大连理工大学数学科学学院,辽宁大连 116085;²大连理工大学船舶工程学院,辽宁大连 116085;³工业装备结构分析国家重点实验室(大连理工大学),辽宁大连 116085

基金项目: 国家自然科学基金（51379033；50921001）；国家重点基础研究计划（2013CB036101；2010CB32700）；中央高校基本科研业务费专项资金（DUT2015LK34；DUT2015LK45）

详细信息

作者简介:
王振（1981—），男，山东人，副教授，博士(通讯作者. E-mail: wangzhen@dlut.edu.cn).

中图分类号: O29;O368
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出版历程
- 收稿日期: 2015-05-13
- 修回日期: 2015-07-08
- 刊出日期: 2015-09-15

Quasi-Periodic Solution and Its Asymptotic Behavior for Camassa-Holm Equation

¹School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116085, P.R.China;²School of Naval Architecture, Dalian University of Technology, Dalian, Liaoning 116085, P.R.China;³State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology), Dalian, Liaoning 116085, P.R.China

Funds: The National Natural Science Foundation of China(51379033；50921001)

摘要

摘要: 近20年来，浅水波模型Camassa-Holm（CH）方程受到诸多研究者关注。在之前的工作中，通过Hirota双线性方法得到了CH方程的单周期解.基于此，该文将对N=2时CH方程的拟周期解及其渐近行为进行研究.首先，回顾了坐标变换，扩展的双线性形式和Riemann(黎曼)θ-函数等内容，并在此基础上利用Hirota双线性方法构造了在N=2时CH方程的含有多个参数的拟周期解，并且此拟周期解是由Riemannθ-函数表示的。其次，发现了此拟周期解渐近行为的一个特点，即CH方程的此拟周期解可以退化为其二孤子解.
- Camassa-Holm方程 /
- 双线性形式 /
- 拟周期解 /
- Riemannθ-函数
Abstract: Many researchers have paid attention to the shallow water wave model Camassa-Holm (CH) equation over the last two decades. The one-periodic solution of CH equation based on the Hirota bilinear method had been presented in our previous work. In this paper, we offer quasi-periodic solution in genus two and its asymptotic behavior. First, we have rearranged the parameters appeared in the bilinear equation system, such as the coordinate transformation, extended bilinear form and Riemman theta function and so on. Then quasi-periodic solution of CH equation is presented, which is expressed by Riemann theta function in genus two. Second, asymptotic behavior of the quasi-periodic solution is discussed. It can be shown that this solution will degenerate into its two-soliton solution.
- Camassa-Holm equation /
- bilinear form /
- quasi-periodic solution /
- Riemman theta function

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参考文献(34)

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