On the Cauchy problem for a new integrable two-component system with peakon and weak kink solutions

Abstract

This paper is contributed to study the Cauchy problem of a new integrable two-component system with peaked soliton (peakon) and weak kink solutions. We first establish the local well-posedness result for the Cauchy problem in Besov spaces, and then present a precise blow-up scenario and a new blow-up result for strong solutions to the system.

arXiv admin note: text overlap with arXiv:1105.1196

References in corpus (6)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• On an integrable two-component Camassa-Holm shallow water system
• Singular solutions of a modified two-component Camassa-Holm equation
• Inverse Scattering Transform for the Degasperis-Procesi Equation
• A new two-component integrable system with peakon solutions
• Integrable system with peakon, weak kink, and kink-peakon interactional solutions