Global Existence for the Derivative Nonlinear Schrödinger Equation with Arbitrary Spectral Singularities

Robert Jenkins, Jiaqi Liu, Peter Perry, Catherine Sulem

Published 2018-04-04, updated 2018-09-05Version 2

We show that the derivative nonlinear Schr\"odinger (DNLS) equation is globally well-posed in the weighted Sobolev space $H^{2,2}(\mathbb{R})$. Our result exploits the complete integrability of DNLS and removes certain spectral conditions on the initial data, thanks to Xin Zhou's analysis on spectral singularities in the context of inverse scattering.