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 $H^1$.

中文翻译：

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广义 Camassa-Holm 方程的周期峰的轨道稳定性

本文研究了广义Camassa-Holm方程的周期性峰值孤子的动力学稳定性。众所周知，它的泛化版本承认单峰孤子解，并在此处显示为具有周期性峰孤子。然后通过构造一个 Lyapunov 泛函，我们推导出周期性 peakon 解在能量空间的小扰动下是轨道稳定的$H^1$.