Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials

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.