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Bifurcation analysis of a two-component Bose–Einstein condensate

✍ Scribed by Yuen-Cheng Kuo; Wen-Wei Lin; Shih-Feng Shieh

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
650 KB
Volume
211
Category
Article
ISSN
0167-2789

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✦ Synopsis

In this paper, we prove that the solution curve of the ground/positive bound states of a two-component Bose-Einstein condensate undergoes supercritical pitchfork bifurcations at some finite values of the inter-component scattering length. The ground state solutions bifurcate into two symmetric solutions with respect to some suitable axis on the symmetric domain, when a twocomponent BEC has equal intra-and inter-component scattering lengths. Furthermore, we show that the ground/positive bound states repel each other and form segregated nodal domains when the repulsive scattering length goes to infinity. Numerical results of bifurcation diagrams and the forms of ground/positive bound state solutions for a two-component BEC with various trap potentials are presented.

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In this paper, we establish a sharp condition of global existence for the solution of twocomponents Bose-Einstein Condensates. This condition is related to the ground state solution of some steady-state two-coupled nonlinear Schrödinger equations.