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arXiv · 1511.01173

Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering

Jiaqi Liu·Peter Perry·Catherine Sulem
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Abstract

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.

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Jiaqi Liu, Peter Perry, Catherine Sulem. 2016-08-14. Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering. https://arxiv.org/abs/1511.01173

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