Analytic well-posedness of periodic gKdV

In the periodic case, it is proved that the Cauchy problem for the generalized Korteweg–de Vries equation (gKdV) is locally well-posed in a class of analytic functions that can be extended holomorphically in a symmetric strip of the complex plane around the x-axis. Thus, 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 provided.