  Considering the coherent nonlinear dynamics in double square well potential
we find the example of coexistence of Josephson oscillations with a
self-trapping regime. This macroscopic bistability is explained by proving
analytically the simultaneous existence of symmetric, antisymmetric and
asymmetric stationary solutions of the associated Gross-Pitaevskii equation.
The effect is illustrated and confirmed by numerical simulations. This property
allows to make suggestions on possible experiments using Bose-Einstein
condensates in engineered optical lattices or weakly coupled optical waveguide
arrays.
