The long-time behaviour for nonlinear Schrödinger equation and its rational pseudospectral approximation

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May 2005, 5(2): 469-488. doi: 10.3934/dcdsb.2005.5.469

The long-time behaviour for nonlinear Schrödinger equation and its rational pseudospectral approximation

1.	Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China

Received December 2003 Revised October 2004 Published February 2005

Abstract
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In this paper, we use the Chebyshev rational pseudospectral method to analyze the long-time behavior of Cauchy problem for nonlinear Schrödinger equation (NSE) with weak damping. We obtain the error estimate of approximate solution and prove the existence and weak upper semicontinuity of approximate attractor.

Keywords: Cauchy problem, approximate attractor., Nonlinear Schrödinger equation, long-time behavior, Chebyshev rational spectral method, global attractor.

Mathematics Subject Classification: 37M99, 65M70, 65N3.

Citation: Xinmin Xiang. The long-time behaviour for nonlinear Schrödinger equation and its rational pseudospectral approximation. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 469-488. doi: 10.3934/dcdsb.2005.5.469

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