Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory

• Main Author: Zhidkov, Peter E. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 1st ed. 2001.
• Series: Lecture Notes in Mathematics, 1756
• Subjects: Partial differential equations.; Mathematical physics.; Partial Differential Equations.; Theoretical, Mathematical and Computational Physics.

- 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 pr...

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.