Differential and Integral Equations

Semi-discrete weakly damped nonlinear 2-D Schrödinger equation

Emna Ezzoug, Olivier Goubet, and Ezzeddine Zahrouni

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Abstract

We consider a semi-discrete in time Crank-Nicolson scheme to discretize a damped forced nonlinear Schrödinger equation in $2D$. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a finite-dimensional global attractor for this dynamical system.

Article information

Source
Differential Integral Equations, Volume 23, Number 3/4 (2010), 237-252.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019316

Mathematical Reviews number (MathSciNet)
MR2588474

Zentralblatt MATH identifier
1240.35512

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35B41: Attractors 37L30: Attractors and their dimensions, Lyapunov exponents

Citation

Ezzoug, Emna; Goubet, Olivier; Zahrouni, Ezzeddine. Semi-discrete weakly damped nonlinear 2-D Schrödinger equation. Differential Integral Equations 23 (2010), no. 3/4, 237--252. https://projecteuclid.org/euclid.die/1356019316


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