Finite‐dimensional global attractor for a semi‐discrete fractional nonlinear Schrödinger equation |
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Authors: | Caterina Calgaro Olivier Goubet Ezzeddine Zahrouni |
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Affiliation: | 1. Univ. Lille, CNRS, UMR 8524 ‐ Laboratoire Paul Painlevé, Lille, France;2. LAMFA UMR 7352 CNRS UPJV, Amiens Cedex, France;3. FSEGN, University of Carthage, Nabeul, Tunisia |
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Abstract: | We consider a semi‐discrete in time Crank–Nicolson scheme to discretize a weakly damped forced nonlinear fractional Schrödinger equation u t ?i (?Δ)α u +i |u |2u +γ u =f for considered in the the whole space . We prove that such semi‐discrete equation provides a discrete infinite‐dimensional dynamical system in that possesses a global attractor in . We show also that if the external force is in a suitable weighted Lebesgue space, then this global attractor has a finite fractal dimension. Copyright © 2017 John Wiley & Sons, Ltd. |
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Keywords: | nonlinear Schrö dinger equations Crank– Nicolson scheme global attractor fractal dimension |
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