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Discrete Schrödinger equations and dissipative dynamical systems

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  • 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.
    Mathematics Subject Classification: 35B41, 35Q55, 65M06.

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