Well-posedness for a coupled system of gKdV equations in analytic spaces

In this article, a Cauchy problem for a coupled system of the generalized Korteweg-de Vries equations (gKdV) is considered. In the periodic case, it is shown that the system is locally well-posed in a large class of analytic functions and conditions for which weak solutions extend holomorphically in a symmetric strip of the complex plane around the $x$-axis at large times. In addition, the uniform analyticity radius of the solution does not change as time progresses. Also, information about the regularity of the solution in the time variable is obtained.