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- catalog abstract "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.".
- catalog contributor b12119058.
- catalog created "2001.".
- catalog date "2001".
- catalog date "2001.".
- catalog dateCopyrighted "2001.".
- catalog description "Includes bibliographical references (p. [137]-146) and index.".
- catalog description "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.".
- catalog description "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.".
- catalog extent "146 p. ;".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540418334 (pbk. : alk. paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1756.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1756".
- catalog issued "2001".
- catalog issued "2001.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 515/. 353 21".
- catalog subject "Differential equations, partial.".
- catalog subject "Korteweg-de Vries equation.".
- catalog subject "Mathematical physics.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1756 QA377".
- catalog subject "Schrödinger equation.".
- catalog tableOfContents "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.".
- catalog title "Korteweg-de Vries and nonlinear Schrodinger equations : qualitative theory / Peter E. Zhidkov.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".