Orbital stability of peakons and multi-peakons for a generalized quintic-septic Camassa-Holm type equation

In this paper, we consider the generalized quintic-septic Camassa-Holm (gqsCH) equation, which is actually an extension of the quintic CH equation and the septic CH equation. We first prove the existence of the single peakon. Then, by constructing certain Lyapunov functionals, we prove the stability of peakons in the energy space H 1 ( R ) H^1(\mathbb {R}) -norm. Finally, we also prove that the sum of N N sufficiently decoupled peakons is orbitally stable in the energy space by using energy argument, combining the method of the orbital stability of single peakons with monotonicity of the local energy norm.