Abstract
The stability of a one-parameter family of dissipative solitons seen in the cubic-quintic complex Ginzburg-Landau equation is studied. It is found that an unusually strong stability occurs for solitons controlled by the spectral filtering and nonlinearity saturation simultaneously, consistently with the linear stability analysis and confirmed by large-perturbation numerical simulations. Two universal types of bifurcations in the spectrum structure are demonstrated.
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