Averaging of Nonlinearity Management with Dissipation
  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. 
S. Beheshti, K. J. H. Law, P. G. Kevrekidis, and Mason A. Porter