Inverse Scattering and Global Well-Posedness in One and Two Space Dimensions

Peter A. Perry

doi:10.1007/978-1-4939-9806-7_4

Inverse Scattering and Global Well-Posedness in One and Two Space Dimensions

Peter A. Perry

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Title of host publication	Fields Institute Communications
Pages	161-252
Number of pages	92
DOIs	https://doi.org/10.1007/978-1-4939-9806-7_4
State	Published - 2019

Publication series

Name	Fields Institute Communications
Volume	83
ISSN (Print)	1069-5265
ISSN (Electronic)	2194-1564

Bibliographical note

Funding 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 [36]— 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. [5], the textbook of Ponce and Linares [34], and the monograph of Trogdon and Olver [43]. This work was supported by a grant from the Simons Foundation/SFARI (359431, PAP).

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.1007/978-1-4939-9806-7_4

Cite this

@inbook{94a7865c57cb43b79f58631f7ce79149,

title = "Inverse Scattering and Global Well-Posedness in One and Two Space Dimensions",

abstract = "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.",

author = "Perry, {Peter A.}",

note = "Funding 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 [36]— 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{\textquoteright}s 2008 course at the Courant Institute on the defocussing NLS equation,6 his 2015 course there on integrable systems,7 and Peter Miller{\textquoteright}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. [5], the textbook of Ponce and Linares [34], and the monograph of Trogdon and Olver [43]. This work was supported by a grant from the Simons Foundation/SFARI (359431, PAP). Publisher Copyright: {\textcopyright} 2019, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

doi = "10.1007/978-1-4939-9806-7_4",

language = "English",

series = "Fields Institute Communications",

pages = "161--252",

booktitle = "Fields Institute Communications",

}

TY - CHAP

T1 - Inverse Scattering and Global Well-Posedness in One and Two Space Dimensions

AU - Perry, Peter A.

N1 - Funding 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 [36]— 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. [5], the textbook of Ponce and Linares [34], and the monograph of Trogdon and Olver [43]. This work was supported by a grant from the Simons Foundation/SFARI (359431, PAP). Publisher Copyright: © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85075512101&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075512101&partnerID=8YFLogxK

U2 - 10.1007/978-1-4939-9806-7_4

DO - 10.1007/978-1-4939-9806-7_4

M3 - Chapter

AN - SCOPUS:85075512101

T3 - Fields Institute Communications

SP - 161

EP - 252

BT - Fields Institute Communications

ER -

Inverse Scattering and Global Well-Posedness in One and Two Space Dimensions

Abstract

Publication series

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this