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Pseudo-Arclength Continuation Algorithms for Binary Rydberg-Dressed Bose-Einstein Condensates

Part of: Partial differential equations, boundary value problems Equations of mathematical physics and other areas of application Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  12 April 2016

Sirilak Sriburadet ,
Y.-S. Wang ,
C.-S. Chien  and
Y. Shih
Sirilak Sriburadet
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, Taichung 402, Taiwan
Y.-S. Wang
Affiliation:
Department of Computer Science and Information Engineering, Chien Hsin University of Science and Technology, Zhongli 320, Taiwan
C.-S. Chien*
Affiliation:
Department of Computer Science and Information Engineering, Chien Hsin University of Science and Technology, Zhongli 320, Taiwan
Y. Shih
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, Taichung 402, Taiwan
*
*Corresponding author. Email addresses:yuijungja@yahoo.com (S. Sriburadet), wang04.wang25@msa.hinet.net (Y.-S. Wang), cschien@uch.edu.tw (C.-S. Chien), Yintzer_Shih@nchu.edu.tw (Y. Shih)
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Abstract

We study pseudo-arclength continuation methods for both Rydberg-dressed Bose-Einstein condensates (BEC), and binary Rydberg-dressed BEC which are governed by the Gross-Pitaevskii equations (GPEs). A divide-and-conquer technique is proposed for rescaling the range/ranges of nonlocal nonlinear term/terms, which gives enough information for choosing a proper stepsize. This guarantees that the solution curve we wish to trace can be precisely approximated. In addition, the ground state solution would successfully evolve from one peak to vortices when the affect of the rotating term is imposed. Moreover, parameter variables with different number of components are exploited in curve-tracing. The proposed methods have the advantage of tracing the ground state solution curve once to compute the contours for various values of the coefficients of the nonlocal nonlinear term/terms. Our numerical results are consistent with those published in the literatures.

Keywords

Ground state solutionsolution branchspectral collocation methoddivide-and-conquer

MSC classification

Secondary: 65N35: Spectral, collocation and related methods 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory 35Q55: NLS-like equations (nonlinear Schrödinger)
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 4 , April 2016 , pp. 1067 - 1093
Copyright
Copyright © Global-Science Press 2016 

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