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arXiv:1902.01009 [math.AP]AbstractReferencesReviewsResources

Inverse scattering and global well-posedness in one and two space dimensions

Peter A. Perry

Published 2019-02-04Version 1

These notes are a considerably revised and expanded version of expository lectures given at the Fields Institute Workshop on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" in August 2017. We give a complete and self-contained treatment of inverse scattering for the defocussing cubic NLS in one-dimension, following the 2003 paper of Deift and Zhou, and the defocussing Davey-Stewartson equation in two space dimensions, following the work of Perry and more recent work of Nachman, Regev, and Tataru.

Comments: 72 pages
Categories: math.AP
Subjects: 37K15, 35Q35, 81U40
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