In this article we prove that the global attractor for a weakly damped nonlinear Schrodinger equation is smooth i.e. it is made of smooth functions when the forcing term is smooth. The proof of this result which is well-known for other dissipative equations does not apply to dispersive equations for which the dissipation is on the low order term. A new simpler proof of existence of this gloabl attractor is given as well.
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