  Motivated by recent experimental studies of matter-waves and optical beams in
double well potentials, we study the solutions of the nonlinear Schr\"{o}dinger
equation in such a context. Using a Galerkin-type approach, we obtain a
detailed handle on the nonlinear solution branches of the problem, starting
from the corresponding linear ones and predict the relevant bifurcations of
solutions for both attractive and repulsive nonlinearities. The results
illustrate the nontrivial differences that arise between the steady
states/bifurcations emerging in symmetric and asymmetric double wells.
