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Journal of Computational Physics

Gauss–Seidel-type methods for energy states of a multi-component Bose–Einstein condensate

Shu-Ming Chang, Wen‐Wei Lin, Shih-Feng Shieh

Published Sep 14, 2004• 58 citations
Publisher
DOI
10.1016/j.jcp.2004.07.012

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•Jul 14, 2009•0 citations
We describe multi-parameter continuation methods combined with spectral collocation methods for computing numerical solutions of rotating two-component Bose–Einstein condensates (BECs), which are governed by the Gross–Pitaevskii equations (GPEs). Various types of orthogonal polynomials are used as the basis functions for the trial function space. A novel multi-parameter/multiscale continuation algorithm is proposed for computing the solutions of the governing GPEs, where the chemical potential of each component and angular velocity are treated as the continuation parameters simultaneously. The proposed algorithm can effectively compute numerical solutions with abundant physical phenomena. Numerical results on rotating two-component BECs are reported.
Three- and five-component nonlinear Schrödinger-type models, which describe spinor Bose-Einstein condensates (BEC's) with hyperfine structures F = 1 and F = 2, respectively, are studied. These models for particular values of the coupling constants are integrable by the inverse scattering method. They are related to symmetric spaces of BD.I-type ≃ SO(2r + 1) / SO(2) × SO(2r -1) for r = 2 and r = 3. Using conveniently modified Zakharov-Shabat dressing procedure we obtain different types of soliton solutions. © 2008 Elsevier B.V. All rights reserved.