Overview
- Includes a nice selection of topics
- Contains a large section of non-standard exercises
- Offers accessible presentation of key tools in harmonic and Fourier analysis
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (10 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research.
Thesecond edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.
Reviews
“This is the second edition of a self-contained graduate level introduction to the results and methods in the well-posedness theory for initial-value problems of nonlinear dispersive equations with special focus on the nonlinear Schrödinger and Korteweg de Vries equations. … I strongly welcome this updated version and I can only recommend it warmly to anybody (both students and teachers) interested in this central area of analysis.” (G. Teschl, Monatshefte für Mathematik, Vol. 180, 2016)
Authors and Affiliations
About the authors
Felipe Linares is a Researcher at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil.
Gustavo Ponce is a Professor of Mathematics at the University of California in Santa Barbara.
Bibliographic Information
Book Title: Introduction to Nonlinear Dispersive Equations
Authors: Felipe Linares, Gustavo Ponce
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4939-2181-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2015
Softcover ISBN: 978-1-4939-2180-5Published: 15 December 2014
eBook ISBN: 978-1-4939-2181-2Published: 15 December 2014
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 2
Number of Pages: XIV, 301
Number of Illustrations: 1 b/w illustrations
Additional Information: 2nd Edition New York, USA 2009
Topics: Partial Differential Equations