$H^2$ solutions for a Degasperis–Procesi-type equation

Abstract

The Degasperis–Procesi equation can be regarded as a model for shallow water dynamics and its asymptotic accuracy is the same as for the Camassa–Holm equation. Here we consider a generalization of the Degasperis–Procesi equation and prove the existence and uniqueness of $H^2$ solutions for the Cauchy problem.