  We consider a class of nonlinear Schrodinger / Gross-Pitaveskii (NLS-GP)
equations, i.e. NLS with a linear potential. We obtain conditions for a
symmetry breaking bifurcation in a symmetric family of states as N, the squared
L^2 norm
  (particle number, optical power), is increased. In the special case where the
linear potential is a double-well with well separation L, we estimate N_{cr},
the symmetry breaking threshold.
  Along the ``lowest energy'' symmetric branch, there is an exchange of
stability from the symmetric to asymmetric branch as N is increased beyond
N_{cr}.
