More Details about Introduction To Nonlinear Dispersive Equations 2nd Edition

General Information  
Author(s)LINARES F
PublisherSPRINGER
Edition2nd Edition
ISBN9781493921805
Pages301
BindingSoftbound
LanguageEnglish
Publish YearFebruary 2015

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 Schroedinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schroedinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schroedinger 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 Schroedinger 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 knowl...