Stability of Peakons for a Nonlinear Generalization of the Camassa-Holm Equation (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, by using the dynamic system method and the knownconservation laws of the gCH equation, and underlying features of the peakons,we study the peakon solutions and the orbital stability of the peakons fora nonlinear generalization of the Camassa-Holm equation (gCH). The gCHequation is first transformed into a planar system. Then, by the first integraland algebraic curves of this system, we obtain one heteroclinic cycle, whichcorresponds to a peakon solution. Moreover, we give a proof of the orbitalstability of the peakons for the gCH equation.