Abstract
We feature the stationary solutions of the 3D complex cubic-quintic Ginzburg-Landau equation (CGLE). Our approach is based on collective variables approach which helps to obtain a system of variational equations, giving the evolution of the light pulses parameters as a function of the propagation distance. The collective variables approach permits us to obtain, efficiently, a global mapping of the 3D stationary dissipative solitons. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics. Thus it helps to show the impact of dispersion and nonlinear gain on the stationary dynamic.
Highlights
Soliton dynamic is one of the most exciting areas of research in nonlinear optics
In conclusions, based on collective variable approach, we have presented the cartography of stationary dissipative solitons modeled by the 3D complex cubic-quintic Ginzburg-Landau equation
We showed that the stationary soliton in this model can be regarded with asymmetric deformations of the pulse in the (x, y) plane
Summary
Soliton dynamic is one of the most exciting areas of research in nonlinear optics. Different phenomena such as nonlinear gain, the saturable losses, the dispersion and others effects are crucial to dissipative solitons formation. We have demonstrated that the collective variables approach is a useful tool and reduces significantly the computation time for predicting approximately the domains of existence of the stationary and pulsating dissipative soliton in the parameters space [9]. This present work provides evidence for the (3D) stationary solutions of the complex cubic-quintic GinzburgLandau equation by the collective variables approach.
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