  In this paper we treat the behavior of Bose Einstein condensates in double
square well potentials, both of equal and different depths. For even depth,
symmetry preserving solutions to the relevant nonlinear Schr\"{o}dinger
equation is known, just as in the linear limit. When the nonlinearity is strong
enough, symmetry breaking solutions also exist, side by side with the symmetric
one. Interestingly, solutions almost entirely localized in one of the wells are
known as an extreme case. Here we outline a method for obtaining all these
solutions for repulsive interactions. The bifurcation point at which, for
critical nonlinearity, the asymmetric solutions branch off from the symmetry
preserving ones is found analytically. We also find this bifurcation point and
treat the solutions generally via a Josephson Junction model.
  When the confining potential is in the form of two wells of different depth,
interesting new phenomena appear. This is true of both the occurrence of the
bifurcation point for the static solutions, and also of the dynamics of phase
and amplitude varying solutions. Again a generalization of the Josephson model
proves useful. The stability of solutions is treated briefly.
