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.
"A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations." Commun. Math. Sci. 5 (2) 299 - 312, June 2007.