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arXiv · 1304.2577

On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity

Xingxing Liu·Zhijun Qiao·Zhaoyang Yin
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Abstract

In this paper, we study the Cauchy problem for a generalized integrable Camassa-Holm equation with both quadratic and cubic nonlinearity. By overcoming the difficulties caused by the complicated mixed nonlinear structure, we firstly establish the local well-posedness result in Besov spaces, and then present a precise blow-up scenario for strong solutions. Furthermore, we show the existence of single peakon by the method of analysis.

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Xingxing Liu, Zhijun Qiao, Zhaoyang Yin. 2013-06-05. On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity. https://arxiv.org/abs/1304.2577

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