Analytical approximation of the soliton solutions of the quintic complex Ginzburg-Landau equation

We have performed a theoretical study of the soliton fiber laser based on the quintic complex Ginzburg-Landau equation (CGLE). This study may also apply to soliton propagation in telecommunications systems. We have developed a simple approach that allows us to obtain, in an approximate way, analytical expressions for the stable pulselike solutions of the CGLE. The method also gives an accurate estimate of the region in the parameter space where stable pulselike solutions exist. We also obtain that the minimum allowed value of the peak amplitude of the soliton solutions depends solely on the relation between the linear loss term and the quintic gain saturation term. The predictions are confirmed by numerical simulations.