A nonlinear generalization of the Camassa-Holm equation with peakon solutions

Abstract

A nonlinearly generalized Camassa-Holm equation, depending an arbitrary nonlinearity power $p\ne 0$, is considered. This equation reduces to the Camassa-Holm equation when $p=1$ and shares one of the Hamiltonian structures of the Camassa-Holm equation. Two main results are obtained. A classification of point symmetries is presented and a peakon solution is derived, for all powers $p\ne 0$.