Introduction to Nonlinear Dispersive Equations

Introduction to Nonlinear Dispersive Equations
Author: Felipe Linares
Publisher: Springer
Total Pages: 308
Release: 2014-12-15
Genre: Mathematics
ISBN: 1493921819


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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.


Introduction to Nonlinear Dispersive Equations
Language: en
Pages: 308
Authors: Felipe Linares
Categories: Mathematics
Type: BOOK - Published: 2014-12-15 - Publisher: Springer

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This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two
Introduction to Nonlinear Dispersive Equations
Language: en
Pages: 263
Authors: Felipe Linares
Categories: Mathematics
Type: BOOK - Published: 2009-02-21 - Publisher: Springer Science & Business Media

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The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are d
Nonlinear Dispersive Equations
Language: en
Pages: 394
Authors: Terence Tao
Categories: Mathematics
Type: BOOK - Published: 2006 - Publisher: American Mathematical Soc.

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"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method
Dispersive Equations and Nonlinear Waves
Language: en
Pages: 310
Authors: Herbert Koch
Categories: Mathematics
Type: BOOK - Published: 2014-07-14 - Publisher: Springer

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The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation an
Mathematical Aspects of Nonlinear Dispersive Equations (AM-163)
Language: en
Pages: 309
Authors: Jean Bourgain
Categories: Mathematics
Type: BOOK - Published: 2009-01-10 - Publisher: Princeton University Press

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This collection of new and original papers on mathematical aspects of nonlinear dispersive equations includes both expository and technical papers that reflect