On the Cauchy problem for the integrable Camassa-Holm type equation with cubic nonlinearity

Details On the Cauchy problem for the integrable Camassa-Holm type equation with cubic nonlinearity On the Cauchy problem for the integrable Camassa-Holm type equation with cubic nonlinearity

2011-08-26

arxiv.org/abs/1108.5368v2

Mathematics

Analysis of PDEs

24 pages

Scientific paper

In this paper, we are concerned with the Cauchy problem for the integrable Camassa-Holm type equation with cubic nonlinearity. We establish the local well-posedness in a range of the Besov spaces and derive the blow-up scenario. With analytic initial data, we then show that its solutions are analytic in both variables, globally in space and locally in time. We also demonstrate nonexistence of the smooth traveling wave solutions. Finally, we give geometric descriptions to this integrable equation.

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