The stationary solutions of G-P equations in double square well

Abstract

We present analytical stationary solutions for the Gross-Pitaevskii equation (GPE) of a Bose-Einstein condensate (BECs) trapped in a double-well potential. These solutions are compared with those described by [Mahmud et al., PRA \textbf{66}, 063607 (2002)]. In particular, we provide further evidence that symmetry preserving stationary solutions can be reduced to the eigenstates of the corresponding linear Schr\"{o}dinger equation. Moreover, we have found that the symmetry breaking solutions can emerge not only from bifurcations, but also from isolated points in the chemical potential-nonlinear interaction diagram. We also have found that there are some moving nodes in the symmetry breaking solutions.