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广义Camassa-Holm方程的行波解

刘小华   

  1. 贵州民族大学理学院, 贵阳, 550025
  • 出版日期:2012-07-25 发布日期:2012-11-16

刘小华. 广义Camassa-Holm方程的行波解[J]. 系统科学与数学, 2012, 32(7): 852-864.

LIU Xiaohua. THE TRAVELING WAVE SOLUTIONS OF THE GENERALIZED CAMASSA-HOLM EQUATION[J]. Journal of Systems Science and Mathematical Sciences, 2012, 32(7): 852-864.

THE TRAVELING WAVE SOLUTIONS OF THE GENERALIZED CAMASSA-HOLM EQUATION

LIU Xiaohua   

  1. School of Science, Guizhou Minzu University, Guiyang 550025
  • Online:2012-07-25 Published:2012-11-16
运用平面动力系统理论和方法给出了广义Camassa-Holm方程在各种参数条件下的相图与分支,分析了奇线对其行波解的影响,获得了广义Camassa-Holm方程光滑、非光滑孤立波解和周期波解的存在性及个数,求出了它的两组新周期尖波解的显式表达式.
In this paper, the existence of the traveling wave solutions to the general-ized Camassa-Holm equation is investigated. For different value of the parameters, the phase diagram and branches of the generalized Camassa-Holm equation are given by the qualitative theory and method of plane dynamic system. The influence of the odd lines on traveling wave solutions of the generalized Camassa-Holm equation is analyzed, the existence and number of smooth, non-smooth solitary wave solutions and periodic wave solutions to the generalized Camassa-Holm equation are obtained. The new exact periodic cusp solutions to the generalized Camassa-Holm equation are found out.

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[1] 王俊杰,王连堂. 一类广义Camassa-Holm方程的多辛Preissmann格式[J]. 系统科学与数学, 2013, 33(11): 1321-1331.
[2] 唐亚宁;徐伟. 一类广义四阶非线性Camassa-Holm方程的行波解[J]. 系统科学与数学, 2008, 28(2): 180-192.
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