Orbital stability of multi-peakons for a generalized Dullin–Gottwald–Holm equation

In this paper, we consider a generalized Dullin–Gottwald–Holm equation. The equation admits single peakons and multi-peakons. Using energy argument and combining the method of the orbital stability of a single peakon with monotonicity of the local energy norm, we prove that the sum of N sufficiently decoupled peakons is orbitally stable in the energy space.