TITLE:
Orbital Stability of Peakons for a Generalized Camassa-Holm Equation
AUTHORS:
Xinhui Lu, Aiyong Chen, Tongjie Deng
KEYWORDS:
Camassa-Holm Equation, Peakon, Heteroclinic Orbit, Orbital Stability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.10,
October
8,
2019
ABSTRACT: 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.