Optical solitons as ground states of NLS in the regime of strong dispersion management

Abstract

The dispersion-managed nonlinear Schrödinger equation (DM-NLS) is considered. After applying an exact transformation, the so-called lens transformation, we derive a new Schrödinger-type equation with additional quadratic potential. In the case of strong dispersion management it is shown how the scales transform into the resulting equation. By constructing ground states of the averaged variational principle we can prove the existence of a standing wave solution of the averaged equation in the case of positive residual dispersion. In contrast to some former discussions of the problem we show the existence of a region where the potential is of trapping type. Due to the potential the solution has a faster decay than the traditional soliton. Moreover we explain why the shape of the DM-soliton changes with increasing pulse energy from a sech-profile to a behavior with Gaussian core and oscillating tails and further to a flatter profile. Furthermore, we illustrate why the DM-soliton can propagate only for small values of the initial pulse width in the case of vanishing or even negative residual dispersion. This results seem to be a new analytical description of what is well known from numerical simulations.