Author(s)

Xinhui Lu¹, Aiyong Chen^1,2, Tongjie Deng¹

¹Department of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China.
²Department of Mathematics, Hunan First Normal University, Changsha, China.

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.

Camassa-Holm Equation, Peakon, Heteroclinic Orbit, Orbital Stability

Lu, X. , Chen, A. and Deng, T. (2019) Orbital Stability of Peakons for a Generalized Camassa-Holm Equation. Journal of Applied Mathematics and Physics, 7, 2200-2211. doi: 10.4236/jamp.2019.710151.