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

• We study an integrable model in the theory of nonlinear shallow-water waves.
• We prove that the sum of finitely many decoupled peakons is orbitally stable.
• We provide an approach to solve the issue caused by the interaction of peakons.

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.