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The complex Ginzburg-Landau equation (CGLE) is a standard model for pulse generation in mode-locked lasers with fast saturable absorbers. We have found complicated pulsating behavior of solitons of the CGLE and regions of their existence in the five-dimensional parameter space. We have found zero-velocity, moving and exploding pulsating localized structures, period doubling (PD) of pulsations and the sequence of PD bifurcations. We have also found 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 certain regions of the parameter space of the CGLE. © 2001 The American Physical SocietyThe work of J.M.S.C. was supported by the Dirección General de Enseñanza Superior under Contract Nos. PB96-0819 and BFM2000-0806, and by the Australian Research Council.Peer Reviewe

Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg-Landau equation approach