Discrete Schrödinger equations and dissipative dynamical systems

Mostafa Abounouh (1) , Hassan Moatassime (1) , Jean-Paul Chehab (2) , Serge Dumont (2) , Olivier Goubet (2)

1 Equipe Equations Aux Derivees Partielles
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We introduce a Crank-Nicolson scheme to study numerically the long-time behavior of solutions to a one dimensional damped forced nonlinear Schrödinger equation. We prove the existence of a smooth global attractor for these discretized equations. We also provide some numerical evidences of this asymptotical smoothing effect.

Mots clés: stability; finite differences; multilevel decomposition

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Mostafa Abounouh, Hassan Moatassime, Jean-Paul Chehab, Serge Dumont, Olivier Goubet. Discrete Schrödinger equations and dissipative dynamical systems. Communications on Pure and Applied Analysis, 2008, 7 (2), pp.211-227. ⟨10.3934/cpaa.2008.7.211⟩. ⟨hal-01113776⟩