  This work deals with soliton solutions of the nonlinear Schroedinger equation
with a diversity of nonlinearities. We solve the equation in a potential which
oscillates in time between attractive and expulsive behavior, in the presence
of nonlinearities which are modulated in space and time. Despite the presence
of the periodically expulsive behavior of the potential, the results show that
the nonlinear equation can support a diversity of localized excitations of the
bright and dark type which are remarkably robust.
