## Advances in Differential Equations

### 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.

#### Article information

Source
Adv. Differential Equations, Volume 22, Number 5/6 (2017), 339-362.

Dates
First available in Project Euclid: 18 March 2017

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