Theory of dissipative solitons in complex Ginzburg-Landau systems.

Using soliton amplitude and phase ansatzes, a theory is proposed for searching for stationary soliton solutions to the cubic-quintic complex Ginzburg-Landau (CGL) equation. For arbitrary combinations of system parameters, our approach allows the existence of dissipative solitons together with their specific soliton characteristics to be determined, and we demonstrate this explicitly for the case of a pulsed fiber laser system. The regimes of existence of dissipative solitons and their rules of evolution in a complicated five-dimensional parameter space are also analyzed. This work may open other research opportunities in diverse areas of nonlinear dynamics governed by the CGL equation, and may impact significantly on experimental design.