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.
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).