Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities

Abstract

We show that the derivative nonlinear Schrödinger (DNLS) equation is globally well-posed in the weighted Sobolev space $H^{2,2}\left(ℝ\right)$. Our result exploits the complete integrability of the DNLS equation and removes certain spectral conditions on the initial data required by our previous work, thanks to Zhou’s analysis (Comm. Pure Appl. Math. 42:7 (1989), 895–938) on spectral singularities in the context of inverse scattering.