Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg-Landau equation approach - art. no. 056602

The complex Ginzburg-Landau equation (CGLE) is a standard model for pulse g eneration in mode-locked lasers with fast saturable absorbers. We have foun d complicated pulsating behavior of solitons of the CGLE and regions of the ir existence in the five-dimensional parameter space. We have found zero-ve locity, moving and exploding pulsating localized structures, period doublin g (PD) of pulsations and the sequence of PD bifurcations. We have also foun d chaotic pulsating solitons. We have plotted regions of parameters of the CGLE where pulsating solutions exist. We also demonstrate the coexistence ( bi- and multistability) of different types of pulsating solutions in certai n regions of the parameter: space of the CGLE.