TY - JOUR
T1 - Bifurcation analysis of a two-component Bose-Einstein condensate
AU - Kuo, Yuen Cheng
AU - Lin, Wen Wei
AU - Shieh, Shih Feng
PY - 2005/11/15
Y1 - 2005/11/15
N2 - 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 two-component 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.
AB - 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 two-component 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.
KW - Bose-Einstein condensate
KW - Gross-Pitaevskii equation
KW - Nonlinear Schrödinger equation
KW - Pitchfork bifurcation
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U2 - 10.1016/j.physd.2005.09.003
DO - 10.1016/j.physd.2005.09.003
M3 - Article
AN - SCOPUS:27644464896
VL - 211
SP - 311
EP - 346
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 3-4
ER -