Mathematics

Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory

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Title (user) : Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative TheoryISBN : 9783540418337,3540418334DOI : 10.1007/3-540-45276-1GoogleBook ID : tO8W7iaVgtgCOpenLibrary ID : OL12774710MEdition : 1Series : Lecture Notes in Mathematics 1756Author...
Description

Title (user) : Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory

ISBN : 9783540418337,3540418334

DOI : 10.1007/3-540-45276-1

GoogleBook ID : tO8W7iaVgtgC

OpenLibrary ID : OL12774710M

Edition : 1

Series : Lecture Notes in Mathematics 1756

Authors (user) : Peter E. Zhidkov (auth.)

Authors (google) : Peter E. Zhidkov

Publisher : Springer-Verlag Berlin Heidelberg

Language : English

Publication Date : 2001

Scanned : yes (300 DPI)

File Format : djvu

Categories : Mathematics


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Description (user) :

- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo- to the observed, example, equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are by known nonlinear At the the class of for same time, currently example [89,94]). see, the other there is solvable this method is narrow on hand, PDEs sufficiently and, by of differential The latter called the another qualitative theory equations. approach, the of various in includes on pr- investigations well-posedness approach particular solutions such or lems for these the behavior of as stability blowing-up, equations, these and this of approach dynamical systems generated by equations, etc., properties in wider class of a makes it to an problems (maybe possible investigate essentially more general study).


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Description (google) :
The emphasis of this book is on questions typical of nonlinear analysis and qualitative theory of PDEs. The selection of the material is related to the author's attempt to illuminate those particularly interesting questions not yet covered in other monographs though they have been the subject of published articles. One chapter, for example, is devoted to the construction of invariant measures for dynamical systems generated by certain equations and a result from a recent paper on basic properties of a system of eigenfunctions of a stationary problem. Also considered is an application of the method of qualitative theory of ODes to proving the existence of radial solutions of stationary problems and stability of solutions of NLSE nonvanishing as the spatial variable tends to infinity. Finally a recent result on the existence of an infinite sequence of invariant measures for the inegrable KdV equation is presented.


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Table of contents :
Introduction....Pages 1-4
Notation....Pages 5-7
Evolutionary equations. Results on existence....Pages 9-38
Stationary problems....Pages 39-78
Stability of solutions....Pages 79-104
Invariant measures....Pages 105-136

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