Overview

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.

Full Product Details

Author:   Peter E. Zhidkov
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2001 ed.
Volume:   1756
Dimensions:   Width: 15.50cm , Height: 0.80cm , Length: 23.50cm
Weight:   0.260kg
ISBN:  

9783540418337

ISBN 10:   3540418334
Pages:   154
Publication Date:   24 April 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Introduction.- Notation.- Evolutionary equations. Results on existance: The (generalized Korteweg-de Vries equation (KdVE); The nonlinear Schrödinger equation (NLSE); On the blowing up of solutions; Additional remarks.- Stationary problems: Existence of solutions. An ODE approach; Existence of solutions. A variational method; The concentration-compactness method of P.L. Lions; On basis properties of systems of solutions; Additional remarks.- Stability of solutions: Stability of soliton-like solutions; Stability of kinks for the KdVE; Stability of solutions of the NLSE nonvanishing as (x) to infinity; Additional remarks.- Invariant measures: On Gaussian measures in Hilbert spaces; An invariant measure for the NLSE; An infinite series of invariant measures for the KdVE; Additional remarks.- Bibliography.- Index.

Reviews

Author Information

Tab Content 6

Author Website:  

Countries Available

All regions