  Motivated by recent experiments in optics and atomic physics, we derive an
averaged nonlinear partial differential equation describing the dynamics of the
complex field in a nonlinear Schroedinger model in the presence of a periodic
nonlinearity and a periodically-varying dissipation coefficient. The
incorporation of dissipation is motivated by experimental considerations. We
test the numerical behavior of the derived averaged equation by comparing it to
the original nonautonomous model in a prototypical case scenario and observe
good agreement between the two.
