Universitext

Introduction to Nonlinear Dispersive Equations

Authors: Linares, Felipe, Ponce, Gustavo

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  • 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
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eBook $59.99
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  • ISBN 978-1-4939-2181-2
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Softcover $74.99
price for USA in USD
  • ISBN 978-1-4939-2180-5
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About this Textbook

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.

The second 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.

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.

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)


Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4939-2181-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-1-4939-2180-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Nonlinear Dispersive Equations
Authors
Series Title
Universitext
Copyright
2015
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4939-2181-2
DOI
10.1007/978-1-4939-2181-2
Softcover ISBN
978-1-4939-2180-5
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XIV, 301
Number of Illustrations
1 b/w illustrations
Additional Information
2nd Edition New York, USA 2009
Topics