Attractor for the nonlinear Schrödinger equation with a nonlocal nonlinear term

In this paper, we consider the long-time behavior of solutions of the dissipative 1D nonlinear Schrödinger (NLS) equation with nonlocal integral term and with periodic boundary conditions. We prove the existence of the global attractor for the nonlocal equation in the strong topology of H 1 (Ω). We...

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Bibliographic Details
Published inJournal of dynamical and control systems Vol. 16; no. 4; pp. 585 - 603
Main Authors Zhu, Chaosheng, Mu, Chunlai, Pu, Zhilin
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.10.2010
Subjects
Boundary conditions
Calculus of Variations and Optimal Control; Optimization
Control
Control systems
Dissipation
Dynamical Systems
Dynamical Systems and Ergodic Theory
Estimates
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Schroedinger equation
Systems Theory
Vibration
global attractor
35B45
35Q55
orthogonal decomposition
35B41
Nonlinear Schrödinger equation
regularity
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Summary:In this paper, we consider the long-time behavior of solutions of the dissipative 1D nonlinear Schrödinger (NLS) equation with nonlocal integral term and with periodic boundary conditions. We prove the existence of the global attractor for the nonlocal equation in the strong topology of H 1 (Ω). We also prove that the global attractor is regular, i.e., , assuming that f ( x ) is of class C 2 . Furthermore, we estimate the number of the determining modes for this equation.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-010-9108-6