Bifurcation Analysis of a Two-Component Bose-Einstein Condensate

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 intraand 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.