An iterative numerical method for dispersion-managed solitons

We present a new numerical method for finding regimes of stable transmission of pulses in nonlinear dispersion-managed (DM) systems. Unlike the known averaging method, whose iterations require finding the pulses with the minimum and maximum width, our method merely starts with an initial guess for the pulse. Even if the initial guess is far from the correct shape, the method rapidly converges to a DM soliton after several iterations. We show that this method is especially relevant for the application to realistic models including filtering and amplification, where the soliton plays the role of an attractor. A new result obtained by means of the iterative method and reported in this work is a global stability region for the solitons in the DM system with lumped filters and amplifiers. We also demonstrate the utility of the method, applying it to a more sophisticated three-step DM system.