Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory
Zhidkov, Peter E.
Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory [electronic resource] / by Peter E. Zhidkov. - X, 154 p. online resource. - Lecture Notes in Mathematics, 1756 0075-8434 ; . - Lecture Notes in Mathematics, 1756 .
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.
- 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).
9783540452768
10.1007/3-540-45276-1 doi
Differential equations, partial.
Partial Differential Equations.
Theoretical, Mathematical and Computational Physics.
QA370-380
515.353
Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory [electronic resource] / by Peter E. Zhidkov. - X, 154 p. online resource. - Lecture Notes in Mathematics, 1756 0075-8434 ; . - Lecture Notes in Mathematics, 1756 .
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.
- 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).
9783540452768
10.1007/3-540-45276-1 doi
Differential equations, partial.
Partial Differential Equations.
Theoretical, Mathematical and Computational Physics.
QA370-380
515.353