A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations

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.

Keywords

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

2010 Mathematics Subject Classification

33C45, 35Q55, 65M70

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Published 1 January 2007