Communications in Mathematical Sciences

Volume 5 (2007)

Number 2

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

Pages: 299 – 312

DOI: http://dx.doi.org/10.4310/CMS.2007.v5.n2.a4

Authors

Juan Pablo Borgna

Peter A. Markowich

Christian Schmeiser

Rada M. Weishäupl

Abstract

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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