Overview
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.
Full Product Details
Author: Felipe Linares ,
Gustavo Ponce
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 2nd ed. 2015
Dimensions:
Width: 15.50cm
, Height: 1.70cm
, Length: 23.50cm
Weight: 4.803kg
ISBN: 9781493921805
ISBN 10: 1493921800
Pages: 301
Publication Date: 15 December 2014
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
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 Schrodinger 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 fur Mathematik, Vol. 180, 2016)
Author Information
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.
