Title:  GLOBAL WELL-POSEDNESS FOR THE DERIVATIVE NONLINEAR SCHR¨ODINGER EQUATION THROUGH INVERSE SCATTERING

Abstract:  We study the Cauchy problem of the derivative nonlinear Schro¨dinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schro¨dinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.