Overview
- 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
Part of the book series: Fields Institute Communications (FIC, volume 83)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (11 chapters)
-
Front Matter
-
Lectures
-
Front Matter
-
-
Research Papers
-
Front Matter
-
Keywords
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.Editors and Affiliations
Bibliographic Information
Book Title: Nonlinear Dispersive Partial Differential Equations and Inverse Scattering
Editors: Peter D. Miller, Peter A. Perry, Jean-Claude Saut, Catherine Sulem
Series Title: Fields Institute Communications
DOI: https://doi.org/10.1007/978-1-4939-9806-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2019
Hardcover ISBN: 978-1-4939-9805-0Published: 14 November 2019
Softcover ISBN: 978-1-4939-9808-1Published: 14 November 2020
eBook ISBN: 978-1-4939-9806-7Published: 14 November 2019
Series ISSN: 1069-5265
Series E-ISSN: 2194-1564
Edition Number: 1
Number of Pages: X, 528
Number of Illustrations: 9 b/w illustrations, 5 illustrations in colour
Topics: Partial Differential Equations
Industry Sectors: Energy, Utilities & Environment, IT & Software