Introduction to nonlinear dispersive equations

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Last edited by MARC Bot
August 12, 2024 | History

Introduction to nonlinear dispersive equations

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.

Publish Date
Publisher
Springer
Language
English
Pages
256

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Previews available in: English

Edition Availability
Cover of: Introduction to nonlinear dispersive equations
Introduction to nonlinear dispersive equations
2015, Springer
in English - Second edition.
Cover of: Introduction to Nonlinear Dispersive Equations
Introduction to Nonlinear Dispersive Equations
Dec 15, 2014, Springer
paperback
Cover of: Introduction to Nonlinear Dispersive Equations
Introduction to Nonlinear Dispersive Equations
2014, Springer London, Limited
in English
Cover of: Introduction to nonlinear dispersive equations
Introduction to nonlinear dispersive equations
2009, Springer
in English

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Book Details


Table of Contents

1. The Fourier transform
2. Interpolation of operators: a multiplier theorem
3. Sobolev spaces and pseudo-differential operators
4. The linear Schrodinger equation
5. The nonlinear Schrodinger equation: local theory
6. Asymptotic behavior for NLS equation
7. Korteweg-de Vries equation
8. Asymptotic behavior for k-gKdV equations
9. Other nonlinear dispersive models
10. General quasilinear Schrodinger equation.

Edition Notes

Includes bibliographical references (p. 239-253) and index.

Published in
New York
Series
Universitext

Classifications

Dewey Decimal Class
530.124
Library of Congress
QA927 .L495 2009, QA1-939

The Physical Object

Pagination
xi, 256 p. ;
Number of pages
256

ID Numbers

Open Library
OL24813856M
Internet Archive
introductiontono00lina
ISBN 10
0387848983, 0387848991
ISBN 13
9780387848983, 9780387848990
LCCN
2008939461
OCLC/WorldCat
258078817

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History

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August 12, 2024 Edited by MARC Bot import existing book
December 13, 2022 Edited by MARC Bot import existing book
December 25, 2021 Edited by ImportBot import existing book
July 1, 2019 Edited by MARC Bot import existing book
July 23, 2011 Created by LC Bot import new book