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 .
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).