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

Rada M. Weishäupl*, Christian Schmeiser, Peter A. Markowich, Juan Pablo Borgna

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)299-312
Number of pages14
JournalCommunications in Mathematical Sciences
Volume5
Issue number2
StatePublished - 2007
Externally publishedYes

Keywords

  • Fourier expansion
  • Gross-Pitaevskii equation
  • Hermite polynomials
  • Spectral decomposition

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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