Orbital stability of periodic peakons for a generalized Camassa–Holm equation

Abstract

The dynamical stability of the periodic peaked solitons for a generalized Camassa–Holm equation is studied in this paper. Its generalization version is known to admit a single-peaked soliton solutions, and is shown here to possess a periodic peakon soliton. Then by constructing a Lyapunov functionals, we derive that the periodic peakon solution is orbitally stable under small perturbations in the energy space $H^1$.

Keywords:

• Generalized Camassa–Holm equation
• periodic peakon
• orbital stability

AMS Subject Classification (2000):

• 35B30
• 35G25

Acknowledgments

The work of Y. Zhang is supported by the National Natural Science Foundation of China (No. 11561059) and Tianshui Normal university ‘Qinglan Talents’ Project.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Tianshui Normal university ‘Qinglan Talents’ Project and National Natural Science Foundation of China [Grant Number 11561059].