Regularization mechanism for the periodic Korteweg deVries equation

Abstract: A successive  averaging method is developed for explaining the regularization mechanism in the periodic Korteweg- deVries (KdV) equation in the homogeneous Sobolev spaces  H^s for s>0.  Specifically, a proof is given of global existence existence, uniqueness, and Lipschitz continuous dependence on the initial data of the solutions of the periodic KdV. For the case  where the initial data is in L_2 we also show the Lipschitz continuous dependence of these solutions with respect to the initial data as maps from H^s to H^s for -1 < s < 0.