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

Olivier Goubet; Ezzeddine Zahrouni

doi:10.3934/cpaa.2008.7.1429

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2008, Volume 7, Issue 6: 1429-1442. Doi: 10.3934/cpaa.2008.7.1429

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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: June 30, 2007

Revised: April 30, 2008

Published: October 2008

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Abstract

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.

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Mathematics Subject Classification: 35Q55, 35B41, 37L30.

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