Classical solutions of the generalized Camassa-Holm equation

Abstract

In this paper, well-posedness in $C^1(\mathbb R)$ (a.k.a. classical solutions) for a generalized Camassa-Holm equation (g-$k$$b$CH) having $(k+1)$-degree nonlinearities is shown. This result holds for the Camassa-Holm, the Degasperis-Procesi and the Novikov equations, which improves upon earlier results in Sobolev and Besov spaces.