Adiabatic amplification of optical solitons

We study the adiabatic evolution of the fundamental nonlinear Schr\"odinger soliton under a general integro-differential perturbation. This perturbation is shown to model a saturable bandwidth-limited amplification of an optical soliton with a nonresonant carrier wave. We use the soliton perturbation theory to calculate the evolution of the amplitude, frequency, group velocity, and phase of the pulse. The perturbative analytical steady-state solution is obtained and its stability is studied using the phase-plane formalism.