Orbital stability of the train of peakons for an integrable modified Camassa-Holm equation

摘要

In this paper, we consider the modified Camassa-Holm equation with cubic nonlinearity, which is integrable and admits the 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.