A determining form for the damped driven nonlinear Schrodinger equation-Fourier modes case

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Jolly, Michael S.¹  Sadigov, Tural¹  Titi, Edriss S.^2,3 

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[2] Weizmann Inst Sci, Dept Appl Math & Comp Sci, IL-76100 Rehovot, Israel

[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

关键词: Nonlinear Schrodinger equation;    Determining forms;    Determining modes;    Determining nodes;    Inertial manifolds;   

DOI  :  10.1016/j.jde.2014.12.023

来源: Elsevier

【 摘 要 】

In this paper we show that the global attractor of the 1D damped, driven, nonlinear Schrodinger equation (NLS) is embedded in the long-time dynamics of a determining form. The determining form is an ordinary differential equation in a space of trajectories X = C-b(1) (R, PmH2) where P-m is the L-2-projector onto the span of the first m Fourier modes. There is a one-to-one identification with the trajectories in the global attractor of the NLS and the steady states of the determining form. We also give an improved estimate for the number of the determining modes. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free