Solution to the double-well nonlinear Schrödinger equation with Stark-type external field

Here we consider one- and two-dimensional nonlinear Schrödinger equations with double well potential and a Stark-type perturbation term. In the semi-classical limit we give an explicit solution to these equations for times of the order of the unperturbed beating period, up to an exponentially small remainder term. In particular, it turns out that the solution has a periodic behavior and the period is explicitly computed.