  In this paper we show numerically that for nonlinear Schrodinger type systems
the presence of nonlocal perturbations can lead to a beyond-all-orders
instability of stable solutions of the local equation. For the specific case of
the nonlocal one-dimensional Gross-Pitaevskii equation with an external
standing light wave potential, we construct exact stationary solutions for an
arbitrary interaction kernel. As the nonlocal and local equations approach each
other (by letting an appropriate small parameter $\epsilon\to 0$), we compare
the dynamics of the respective solutions. By considering the time of onset of
instability, the singular nature of the inclusion of nonlocality is
demonstrated, independent of the form of the interaction kernel.
