On a time discretization of a weakly damped forced nonlinear Schrödinger equation

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November 2008, 7(6): 1429-1442. doi: 10.3934/cpaa.2008.7.1429

On a time discretization of a weakly damped forced nonlinear Schrödinger equation

Olivier Goubet ^1, and Ezzeddine Zahrouni ^2,

1.	Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex
2.	Department de Mathematiques, Faculte des Sciences de Monastir , 5000 MONASTIR

Received July 2007 Revised May 2008 Published August 2008

Abstract
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We consider a semi-discrete in time Crank-Nicolson scheme to discretize a damped forced nonlinear Schrödinger equation. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a finite dimensional global attractor for this dynamical system.

Keywords: nonlinear Schrödinger equations., Global Attractor, Crank-Nicolson scheme.

Mathematics Subject Classification: 35Q55, 35B41, 37L3.

Citation: Olivier Goubet, Ezzeddine Zahrouni. On a time discretization of a weakly damped forced nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1429-1442. doi: 10.3934/cpaa.2008.7.1429

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