# Advances in Analysis

### Global Attractor of Nonlocal Nonlinear Schrödinger Equation on R

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### Author(s)

**Chaosheng Zhu**^{*}

School of mathematics and statistics, Southwest University, Chongqing, 400715, P. R. China.

### Abstract

_{r}in the strong topology of H

^{1}(R) and the existence of the exponential attractor M which contains the global attractor A , are still finite dimensional, and attract the trajectories exponentially fast. We also show that the global attractor A

_{r}is regular, i.e., A

_{r}is included, bounded and compact in H

^{2}(R) assuming that the forcing term f(x) is of class H

^{2}(R). Furthermore we estimate the number of the determining modes for this equation. Moreover, we show that the solution trajectories and the global attractor of the nonlocal Schrödinger equation converge to those of the usual Schrödinger equation, as the coefficient of the nonlocal integral term goes to zero.

### Keywords

### References

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