Vol. 13, No. 5, 2020

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

Robert Jenkins, Jiaqi Liu, Peter Perry and Catherine Sulem

Vol. 13 (2020), No. 5, 1539–1578
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.

Keywords
derivative nonlinear Schrödinger, inverse scattering, global well-posedness
Mathematical Subject Classification 2010
Primary: 35Q55, 37K15
Secondary: 35P25, 35R30