Nonlinear dispersive partial differential equations and inverse scattering /

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Bibliographic Details
Imprint:New York, NY : Springer, 2019.
Description:1 online resource (x, 528 pages) : illustrations (some color).
Language:English
Series:Fields Institute communications, 1069-5265 ; volume 83
Fields Institute communications ; v. 83.
Subject:Differential equations, Partial.
Inverse scattering transform.
Differential equations, Partial.
Inverse scattering transform.
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11997604
Hidden Bibliographic Details
Other authors / contributors:Miller, Peter D. editor.
Perry, Peter A., editor.
Saut, J.-C. (Jean-Claude), editor.
Sulem, C. (Catherine), 1957- editor.
ISBN:9781493998067
1493998064
9781493998050
1493998056
Notes:Online resource; title from PDF title page (SpringerLink, viewed November 18, 2019).
Summary:This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deifts Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing nonlinear SchroŐądinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions. The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.
Other form:Print version: 1493998056 9781493998050
Standard no.:10.1007/978-1-4939-9806-7
10.1007/978-1-4939-9