Optical soliton perturbation with Raman scattering and saturable amplifiers

The method of multiple-scale perturbation is developed to study the propagation of solitons through an optical fiber described by the perturbed nonlinear Schrödinger's equation. We show that, by introducing a proper definition of the phase of the soliton, one can obtain the corrections to the pulse where the usual soliton perturbation approach fails. A comparison is made with results obtained by other methods as well as with numerical simulations.