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Fields Institute Communications

Nonlinear Dispersive Partial Differential Equations and Inverse Scattering

Editors: Miller, P.D., Perry, P., Saut, J.-C., Sulem, C. (Eds.)

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  • Contains pioneering works that establish the "nonlinear steepest descent" method for solving the Riemann-Hilbert problems at the heart of inverse scattering
  • Provides an introduction and overview of the completely integral method and its applications in dynamical systems, probability, statistical mechanics, and other areas
  • Features a comprehensive survey of results for the Benjamin-Ono and Intermediate Long-Wave equations
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About this book

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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook 85,59 €
price for Spain (gross)
  • ISBN 978-1-4939-9806-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-1-4939-9805-0
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Dispersive Partial Differential Equations and Inverse Scattering
Editors
  • Peter D. Miller
  • Peter Perry
  • Jean-Claude Saut
  • Catherine Sulem
Series Title
Fields Institute Communications
Series Volume
83
Copyright
2019
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC, part of Springer Nature
eBook ISBN
978-1-4939-9806-7
DOI
10.1007/978-1-4939-9806-7
Hardcover ISBN
978-1-4939-9805-0
Series ISSN
1069-5265
Edition Number
1
Number of Pages
X, 528
Number of Illustrations
9 b/w illustrations, 5 illustrations in colour
Topics

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