A continuation BSOR-Lanczos-Galerkin method for positive bound states of a multi-component Bose-Einstein condensate

Shu Ming Chang, Yuen Cheng Kuo, Wen Wei Lin, Shih-Feng Shieh

Research output: Contribution to journalArticle

11 Citations (Scopus)


We develop a continuation block successive over-relaxation (BSOR)-Lanczos-Galerkin method for the computation of positive bound states of time-independent, coupled Gross-Pitaevskii equations (CGPEs) which describe a multi-component Bose-Einstein condensate (BEC). A discretization of the CGPEs leads to a nonlinear algebraic eigenvalue problem (NAEP). The solution curve with respect to some parameter of the NAEP is then followed by the proposed method. For a single-component BEC, we prove that there exists a unique global minimizer (the ground state) which is represented by an ordinary differential equation with the initial value. For a multi-component BEC, we prove that m identical ground/bound states will bifurcate into m different ground/bound states at a finite repulsive inter-component scattering length. Numerical results show that various positive bound states of a two/three-component BEC are solved efficiently and reliably by the continuation BSOR-Lanczos-Galerkin method.

Original languageEnglish
Pages (from-to)439-458
Number of pages20
JournalJournal of Computational Physics
Issue number2
Publication statusPublished - 2005 Dec 10



  • Continuation BSOR-Lanczos-Galerkin method
  • Gauss-Seidel-type iteration
  • Gross-Pitaevskii equation
  • Multi-component Bose-Einstein condensate
  • Nonlinear Schrödinger equation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this