On the Gross-Pitaevskii equation with strongly anisotropic confinement: Formal asymptotics and numerical experiments

Weizhu Bao*, Peter Markowich, Christian Schmeiser, Rada M. Weishäupl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

The three-dimensional (3D) Gross-Pitaevskii equation with strongly anisotropic confining potential is analyzed. The formal limit as the ratio of the frequencies ε tends to zero provides a denumerable system of two-dimensional Gross-Pitaevskii equations, strongly coupled through the cubic nonlinearities. To numerically solve the asymptotic approximation only a finite number of limiting equations is considered. Finally, the approximation error for a fixed number of equations is compared for different ε tending to zero. On the other hand, the approximation error for an increasing number of terms in the approximation is observed.

Original languageEnglish (US)
Pages (from-to)767-782
Number of pages16
JournalMathematical Models and Methods in Applied Sciences
Volume15
Issue number5
DOIs
StatePublished - May 1 2005

Keywords

  • Approximation error
  • Fourier expansion
  • Gross-Pitaevskii equation
  • Spectral decomposition
  • Time splitting-spectral techniques

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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