Orbital Stability of Peakons for a Generalized Camassa-Holm Equation

Orbital Stability of Peakons for a Generalized Camassa-Holm Equation
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DOI：
10.4236/jamp.2019.710151
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发表时间：
2019-10
期刊：
Journal of Applied Mathematics and Physics
影响因子：
--
通讯作者：
Xinhui Lu;Aiyong Chen;Tongjie Deng
Xinhui Lu;Aiyong Chen;Tongjie Deng
中科院分区：
其他
文献类型：
--
作者：
Xinhui Lu;Aiyong Chen;Tongjie Deng

文献摘要

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研究了广义Camassa-Holm方程（gCH）峰子的轨道稳定性.利用变量变换，从gCH方程得到一个平面动力系统.证明了平面系统存在两个异宿环，对应两个峰子解。利用Constantin和Strauss方法证明了gCH方程的峰子是轨道稳定的。
We investigate the orbital stability of the peakons for a generalized Camassa-Holm equation (gCH). Using variable transformation, a planar dynamical system is obtained from the gCH equation. It is shown that the planar system has two heteroclinic cycles which correspond two peakon solutions. We then prove that the peakons for the gCH equation are orbitally stable by using the method of Constantin and Strauss.