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

  • Authors:

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

  • Affiliations:

  • Department of Mathematics, National Tsing Hua University, 101 Sec. 2, Kuang Fu Rd., Hsinchu 30043, Taiwan;Department of Mathematics, National Tsing Hua University, 101 Sec. 2, Kuang Fu Rd., Hsinchu 30043, Taiwan;Department of Mathematics, National Tsing Hua University, 101 Sec. 2, Kuang Fu Rd., Hsinchu 30043, Taiwan;Department of Mathematics, National Tsing Hua University, 101 Sec. 2, Kuang Fu Rd., Hsinchu 30043, Taiwan

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

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.