We develop inverse scattering for the derivative nonlinear Schrodinger equation (DNLS) on the line using its gauge equivalence with a related nonlinear dispersive equation. We prove Lipschitz continuity of the direct and inverse scattering maps from the weighted Sobolev spaces $H^{ 2,2}(\mathbb{ R})$ to itself. These results immediately imply global existence of solutions to the DNLS for initial data in a spectrally determined (open) subset of $H^{ 2,2}(\mathbb{ R})$ containing a neighborhood of 0.
Categories: math.AP