Dissipative Solitons in the Complex Ginzburg-Landau Equation for Femtosecond Lasers

We consider the models of generating femtosecond radiation in solid-state lasers with passive mode locking. An approach in which ultrashort laser pulses (USPs) are associated with the complex Ginzburg-Landau equation (GLE) is developed. The structure of solitons and the range of parameters of their existence are analytically determined and the stability criteria of those solitons are formulated for a number of limiting cases. The scenarios of the cyclic spectral and temporal dynamics of dissipative solitons due to the instability of the background field are studied.