Commun. Comput. Phys., 13 (2013), pp. 442-460.


A Two-Parameter Continuation Method for Rotating Two-Component Bose-Einstein Condensates in Optical Lattices

Y.-S. Wang 1, B.-W. Jeng 2, C.-S. Chien 3*

1 Department of Applied Mathematics, National Chung Hsing University, Taichung 402, Taiwan.
2 Department of Mathematics Education, National Taichung University of Education, Taichung 403, Taiwan.
3 Department of Computer Science and Information Engineering, Ching Yun University, Jungli 320, Taiwan.

Received 11 July 2011; Accepted (in revised version) 17 February 2012
Available online 28 June 2012
doi:10.4208/cicp.110711.170212a

Abstract

We study efficient spectral-collocation and continuation methods (SCCM) for rotating two-component Bose-Einstein condensates (BECs) and rotating two-component BECs in optical lattices, where the second kind Chebyshev polynomials are used as the basis functions for the trial function space. A novel two-parameter continuation algorithm is proposed for computing the ground state and first excited state solutions of the governing Gross-Pitaevskii equations (GPEs), where the classical tangent vector is split into two constraint conditions for the bordered linear systems. Numerical results on rotating two-component BECs and rotating two-component BECs in optical lattices are reported. The results on the former are consistent with the published numerical results.

AMS subject classifications: 65N35, 35P30, 35Q55

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Key words: Spectral collocation method, second kind Chebyshev polynomials, periodic potential, bifurcation.

*Corresponding author.
Email: wang04.wang25@msa.hinet.net (Y.-S. Wang), bwjeng@mail.ntcu.edu.tw (B.-W. Jeng), cschien@cyu.edu.tw, cschien@amath.nchu.edu.tw (C.-S. Chien)
 

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