On dispersion managed nonlinear Schrödinger equations with lumped amplification

Abstract: We show the global well-posedness of the nonlinear Schr\"odinger equation with periodically varying coefficients and a small parameter $\varepsilon>0$, which is used in optical-fiber communications. We also prove that the solutions converge to the solution for the Gabitov-Turitsyn or averaged equation as $\varepsilon$ tends to zero.