The Cauchy problem for an integrable two-component model with peakon solutions

Abstract

In this paper, we are concerned with the Cauchy problem of the new integrable two-componnt system with cubic non-linearity, which was proposed by Xia, Qiao and Zhou. We establish the local well-posedness in a range of the Besov spaces. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time.

Keywords:

• Besov spaces
• Camassa–Holm-type equation
• local well-posedness

AMS Subject Classifications:

• 35B30
• 35G25
• 35A10
• 35Q53

Acknowledgments

This work was partially supported by NSF of China (11071266), partially supported by Scholarship Award for Excellent Doctoral Student granted by Ministry of Education and partially supported by the Educational Science Foundation of Chongqing China(KJ121302).