On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity
Analysis of PDEs
2013-06-06 v2
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.
Keywords
Cite
@article{arxiv.1304.2577,
title = {On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity},
author = {Xingxing Liu and Zhijun Qiao and Zhaoyang Yin},
journal= {arXiv preprint arXiv:1304.2577},
year = {2013}
}