Orbital Stability of Peakons and Multi-peakons for a Generalized Cubic–Quintic Camassa–Holm Type Equation

Abstract

AbstractThe peakons and mulit-peakons for a generalized cubic–quintic Camassa–Holm type equation have been obtained by Weng et al. (Monatsh Math, 2022. https://doi.org/10.1007/s00605-022-01699-w). In this paper, by constructing certain Lyapunov functionals, we prove that the peakons were orbitally stable in the energy space. Furthermore, using energy argument and combining the method of the orbital stability of peakons with monotonicity of the local energy norm, we also prove that the sum of N sufficiently decoupled peakons is orbitally stable in the energy space.