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Classical solutions of the generalized Camassa-Holm equation. (English) Zbl 1364.35310

Summary: In this paper, well-posedness in \(C^1(\mathbb R)\) (a.k.a. classical solutions) for a generalized Camassa-Holm equation \((g-kb \mathrm {CH})\) 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.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A09 Classical solutions to PDEs
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Full Text: Euclid