Orbital Stability of the Sum of $N$ Peakons for the CH-mCH Equation

Abstract

This paper is concerned with a generalization of the modified Camassa-Holm equation with both cubic and quadratic nonlinearities (also known as the CH-mCH equation). We mainly prove the orbital stability of the train of peakons for the CH-mCH equation in energy space, using energy arguments and combining the method of orbital stability of a single peakon with the monotonicity of the local energy norm.