Differential and Integral Equations

Semi-discrete weakly damped nonlinear 2-D Schrödinger equation

Emna Ezzoug, Olivier Goubet, and Ezzeddine Zahrouni

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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

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

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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