Year: 2011
East Asian Journal on Applied Mathematics, Vol. 1 (2011), Iss. 1 : pp. 49–81
Abstract
In this paper, we prove existence and uniqueness results for the ground states of the coupled Gross-Pitaevskii equations for describing two-component Bose-Einstein condensates with an internal atomic Josephson junction, and obtain the limiting behavior of the ground states with large parameters. Efficient and accurate numerical methods based on continuous normalized gradient flow and gradient flow with discrete normalization are presented, for computing the ground states numerically. A modified backward Euler finite difference scheme is proposed to discretize the gradient flows. Numerical results are reported, to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomena of the ground sates in the problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.190310.170510a
East Asian Journal on Applied Mathematics, Vol. 1 (2011), Iss. 1 : pp. 49–81
Published online: 2011-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Bose-Einstein condensate coupled Gross-Pitaevskii equations two-component ground state normalized gradient flow internal atomic Josephson junction energy.
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