Advances in Differential Equations

Classical solutions of the generalized Camassa-Holm equation

John Holmes and Ryan C. Thompson

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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

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

First available in Project Euclid: 18 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]


Holmes, John; Thompson, Ryan C. Classical solutions of the generalized Camassa-Holm equation. Adv. Differential Equations 22 (2017), no. 5/6, 339--362.

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