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arXiv · 1704.00071

Global existence for the derivative NLS equation in the presence of solitons

Aaron Saalmann
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Abstract

We prove the existence of global solutions to the DNLS equation with initial data in a large subset of $H^2(\mathbb R)\cap H^{1,1}(\mathbb R)$ containing a neighborhood of all solitons. We use the inverse scattering transform method, which was recently developed by D. Pelinovsky and Y. Shimabukuro, and an auto-Bäcklund transform in order to include solitons.

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Aaron Saalmann. 2017-08-05. Global existence for the derivative NLS equation in the presence of solitons. https://arxiv.org/abs/1704.00071

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