Bright and dark solitons in a periodically attractive and expulsive potential with nonlinearities modulated in space and time

This work deals with soliton solutions of the nonlinear Schrödinger 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 types.