Stable Soliton Propagation in a System with Spectral Filtering and Nonlinear Gain

Stable soliton propagation in a system with linear and nonlinear gain and spectral filtering is investigated. Different types of exact analytical solutions of the cubic and the quintic complex Ginzburg-Landau equation (CGLE) are reviewed. The conditions to achieve stable soliton propagation are analyzed within the domain of validity of soliton perturbation theory. We derive an analytical expression defining the region in the parameter space where stable pulselike solutions exist, which agrees with the numerical results obtained by other authors. An analytical expression for the soliton amplitude corresponding to the quintic CGLE is also obtained. We show that the minimum value of this amplitude depends only on the ratio between the linear gain and the quintic gain saturating term.