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Nonlinear dispersive partial differential equations and inverse scattering

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 an...

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Autores principales: Miller, Peter, Perry, Peter, Saut, Jean-Claude, Sulem, Catherine
Lenguaje:eng
Publicado: Springer 2019
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-1-4939-9806-7
http://cds.cern.ch/record/2704085
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author Miller, Peter
Perry, Peter
Saut, Jean-Claude
Sulem, Catherine
author_facet Miller, Peter
Perry, Peter
Saut, Jean-Claude
Sulem, Catherine
author_sort Miller, Peter
collection CERN
description 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 Deift’s 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 Schrödinger (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.
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spelling cern-27040852021-04-21T18:14:34Zdoi:10.1007/978-1-4939-9806-7http://cds.cern.ch/record/2704085engMiller, PeterPerry, PeterSaut, Jean-ClaudeSulem, CatherineNonlinear dispersive partial differential equations and inverse scatteringMathematical Physics and MathematicsThis 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 Deift’s 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 Schrödinger (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.Springeroai:cds.cern.ch:27040852019
spellingShingle Mathematical Physics and Mathematics
Miller, Peter
Perry, Peter
Saut, Jean-Claude
Sulem, Catherine
Nonlinear dispersive partial differential equations and inverse scattering
title Nonlinear dispersive partial differential equations and inverse scattering
title_full Nonlinear dispersive partial differential equations and inverse scattering
title_fullStr Nonlinear dispersive partial differential equations and inverse scattering
title_full_unstemmed Nonlinear dispersive partial differential equations and inverse scattering
title_short Nonlinear dispersive partial differential equations and inverse scattering
title_sort nonlinear dispersive partial differential equations and inverse scattering
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-1-4939-9806-7
http://cds.cern.ch/record/2704085
work_keys_str_mv AT millerpeter nonlineardispersivepartialdifferentialequationsandinversescattering
AT perrypeter nonlineardispersivepartialdifferentialequationsandinversescattering
AT sautjeanclaude nonlineardispersivepartialdifferentialequationsandinversescattering
AT sulemcatherine nonlineardispersivepartialdifferentialequationsandinversescattering