These notes are a considerably revised and expanded version of lectures given at the Fields Institute workshop on “Nonlinear Dispersive Partial Differential Equations and Inverse Scattering” in August 2017. These lectures, together with lectures of Walter Craig, Patrick Gerard, Peter D. Miller, and Jean-Claude Saut, constituted a week-long introduction to recent developments in inverse scattering and dispersive PDE intended for students and postdoctoral researchers working in these two areas.
|Title of host publication||Fields Institute Communications|
|Number of pages||92|
|State||Published - 2019|
|Name||Fields Institute Communications|
Bibliographical noteFunding Information:
I am grateful to the University of Kentucky for sabbatical support during part of the time these lectures were prepared, and to Adrian Nachman and Idan Regev for many helpful discussions about their work. I thank the participants in a Fall 2017 working seminar on — Russell Brown, Joel Klipfel, George Lytle, and Mihai Tohaneanu—for helping me understand this paper in greater depth. I have benefited from conversations with Deniz Bilman about Lax representations and Riemann-Hilbert problems. I have also benefited from course notes for Percy Deift’s 2008 course at the Courant Institute on the defocussing NLS equation,6 his 2015 course there on integrable systems,7 and Peter Miller’s Winter 2018 course at the University of Michigan on integrable systems and Riemann-Hilbert problems.8 For supplementary material, I have drawn on several excellent sources for material on dispersive equations, Riemann-Hilbert problems, and ∂-problems, namely the monograph of Astala et al. , the textbook of Ponce and Linares , and the monograph of Trogdon and Olver . This work was supported by a grant from the Simons Foundation/SFARI (359431, PAP).
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ASJC Scopus subject areas
- Mathematics (all)