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Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect

Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect,10.1016/j.amc.2011.02.096,Applied Mathemati

Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect  
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We consider a semi-discrete in time Crank-Nicolson scheme to discretize a weakly-damped forced nonlinear Schrödinger equation with a delta-function impurity in one space dimension. We prove that such a semi-discrete equation provides a discrete infinite dimensional dynamical system in H1(R) that possesses a global attractor in H1(R). We show also that this global attractor is actually a compact set of H32-ε(R) and has a finite fractal dimension.
Journal: Applied Mathematics and Computation - AMC , vol. 217, no. 19, pp. 7818-7830, 2011
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