The long-time behaviour for nonlinear Schr&ouml;dinger equation and its rational pseudospectral approximation

Xinmin Xiang

doi:10.3934/dcdsb.2005.5.469

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2005, Volume 5, Issue 2: 469-488. Doi: 10.3934/dcdsb.2005.5.469

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

Xinmin Xiang^1,

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

Received: December 2003

Revised: October 2004

Published: May 2008

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Abstract

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.

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Mathematics Subject Classification: 37M99, 65M70, 65N35.

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