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

2013/04/09 by Liu, Xingxing, Qiao, Zhijun, Yin, Zhaoyang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1304.2577

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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