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 .
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