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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

王振, 秦玉鹏, 邹丽, 马瑞芳, 朱贵勋. Camassa-Holm方程的拟周期解及其渐近行为[J]. 应用数学和力学, 2015, 36(9): 990-1002. doi: 10.3879/j.issn.1000-0887.2015.09.010
引用本文: 王振, 秦玉鹏, 邹丽, 马瑞芳, 朱贵勋. Camassa-Holm方程的拟周期解及其渐近行为[J]. 应用数学和力学, 2015, 36(9): 990-1002. doi: 10.3879/j.issn.1000-0887.2015.09.010
WANG Zhen, QIN Yu-peng, ZOU Li, MA Rui-fang, ZHU Gui-xun. Quasi-Periodic Solution and Its Asymptotic Behavior for Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2015, 36(9): 990-1002. doi: 10.3879/j.issn.1000-0887.2015.09.010
Citation: WANG Zhen, QIN Yu-peng, ZOU Li, MA Rui-fang, ZHU Gui-xun. Quasi-Periodic Solution and Its Asymptotic Behavior for Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2015, 36(9): 990-1002. 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
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

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

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

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