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Well posedness for a higher order modified Camassa-Holm equation. (English) Zbl 1170.35087
Summary: We show that the Cauchy problem for a higher order modification of the Camassa-Holm equation is locally well posed for initial data in the Sobolev space $H^s(\Bbb R)$ for $s>s{^{\prime}}$, where $1/4\leqslant s{^{\prime}}<1/2$ and the value of $s{^{\prime}}$ depends on the order of equation. Employing harmonic analysis methods we derive the corresponding bilinear estimate and then use a contraction mapping argument to prove existence and uniqueness of solutions.

MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35A20 Analytic methods, singularities (PDE) 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text:
References:
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