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

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.

References in corpus (2)

• Integrable system with peakon, weak kink, and kink-peakon interactional solutions
• Smooth soliton solutions of a new integrable equation by Qiao

Cited by in corpus (1)

• Stability of peakons for a modified Camassa-Holm equation