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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 mat...

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Detalles Bibliográficos
Autores principales: Linares, Felipe, Ponce, Gustavo
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-1-4939-2181-2
http://cds.cern.ch/record/1980569
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author Linares, Felipe
Ponce, Gustavo
author_facet Linares, Felipe
Ponce, Gustavo
author_sort Linares, Felipe
collection CERN
description 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.
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spelling cern-19805692021-04-21T20:38:15Zdoi:10.1007/978-1-4939-2181-2http://cds.cern.ch/record/1980569engLinares, FelipePonce, GustavoIntroduction to nonlinear dispersive equationsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:19805692015
spellingShingle Mathematical Physics and Mathematics
Linares, Felipe
Ponce, Gustavo
Introduction to nonlinear dispersive equations
title Introduction to nonlinear dispersive equations
title_full Introduction to nonlinear dispersive equations
title_fullStr Introduction to nonlinear dispersive equations
title_full_unstemmed Introduction to nonlinear dispersive equations
title_short Introduction to nonlinear dispersive equations
title_sort introduction to nonlinear dispersive equations
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-1-4939-2181-2
http://cds.cern.ch/record/1980569
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