Numerical simulation of the nonlinear schrödinger equation with multidimensional periodic potentials

Zhongyi Huang*, Shi Jin, Peter Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

By extending the Bloch-decomposition-based time-splitting spectral method we introduced earlier, we conduct numerical simulations of the dynamics of nonlinear Schrodingerequations subject to periodic and confining potentials. We consider this system as a two-scale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present three-dimensional simulations for lattic Bose-Einstein condensates in the superfluid regime.

Original languageEnglish (US)
Pages (from-to)539-564
Number of pages26
JournalMultiscale Modeling and Simulation
Volume7
Issue number2
DOIs
StatePublished - Jan 1 2008

Keywords

  • Bloch decomposition
  • Bose
  • Einstein condensates
  • Fermi approximation
  • Lattice potential
  • Onlinear Schrodinger equation
  • Splitting spectral method
  • Thomas
  • time

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

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