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.
@article{1183990367,
author = {Weish\"aupl, Rada M. and Schmeiser, Christian and Markowich, Peter A. and Borgna, Juan Pablo},
title = {A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations},
journal = {Commun. Math. Sci.},
volume = {5},
number = {1},
year = {2007},
pages = { 299-312},
language = {en},
url = {http://dml.mathdoc.fr/item/1183990367}
}
Weishäupl, Rada M.; Schmeiser, Christian; Markowich, Peter A.; Borgna, Juan Pablo. A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations. Commun. Math. Sci., Tome 5 (2007) no. 1, pp. 299-312. http://gdmltest.u-ga.fr/item/1183990367/