  Gross-Pitaevskii and nonlinear Hartree equations are equations of nonlinear
Schroedinger type, which play an important role in the theory of Bose-Einstein
condensation. Recent results of Aschenbacher et. al. [AFGST] demonstrate, for a
class of 3- dimensional models, that for large boson number (squared L^2 norm),
N, the ground state does not have the symmetry properties as the ground state
at small N. We present a detailed global study of the symmetry breaking
bifurcation for a 1-dimensional model Gross-Pitaevskii equation, in which the
external potential (boson trap) is an attractive double-well, consisting of two
attractive Dirac delta functions concentrated at distinct points. Using
dynamical systems methods, we present a geometric analysis of the symmetry
breaking bifurcation of an asymmetric ground state and the exchange of
dynamical stability from the symmetric branch to the asymmetric branch at the
bifurcation point.

Pattern Formation and Solitons;Adaptation and Self-Organizing Systems