Global Existence for the Derivative Nonlinear Schr\"{o}dinger Equation with Arbitrary Spectral Singularities

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.