Orbital Stability of Peakons for a Generalized Camassa-Holm Equation
Xinhui LuDepartment of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, ChinaAiyong ChenDepartment of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, ChinaTongjie DengDepartment of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
2019en
ABI
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.
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