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June 2007 A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations
Rada M. Weishäupl, Christian Schmeiser, Peter A. Markowich, Juan Pablo Borgna
Commun. Math. Sci. 5(2): 299-312 (June 2007).


We propose and analyze discretization methods for solving finite systems of nonlinearly coupled Schrödinger equations, which arise as an asymptotic limit of the three-dimensional Gross-Pitaevskii equation with strongly anisotropic potential. A pseudo-spectral method with Hermite basis functions combined with a Crank-Nicolson type method is introduced. Numerical experiments are presented, including a comparison with an alternative discretization approach.


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Rada M. Weishäupl. Christian Schmeiser. Peter A. Markowich. Juan Pablo Borgna. "A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations." Commun. Math. Sci. 5 (2) 299 - 312, June 2007.


Published: June 2007
First available in Project Euclid: 9 July 2007

zbMATH: 1151.35087
MathSciNet: MR2334844

Primary: 33C45 , 35Q55 , 65M70

Keywords: Fourier expansion , Gross-Pitaevskii equation , Hermite polynomials , spectral decomposition

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 2 • June 2007
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