Gyroelectric cubic-quintic dissipative solitons

The influence of an externally applied magnetic field upon classic cubic quintic dissipative solitons is investigated using both exact simulations and a Lagrangian technique. The basic approach is to use a spatially inhomogeneous magnetic field and to consider two important geometries, namely the Voigt and the Faraday effects. A layered structure is selected for the Voigt case, with the principal aim being to demonstrate nonreciprocal behavior for various classes of spatial solitons that are known to exist as solutions of the complex Ginzburg-Landau cubic-quintic envelope equation under dissipative conditions. The system is viewed as dynamical, and we display the behavior patterns of the spatial solitons in terms of two-dimensional dynamical plots involving the total energy and the peak amplitude of the spatial solitons. This leads to limit cycle plots that beautifully reveal the behavior of the solitons solutions at all points along the propagation axis. The closed contour that exists in the absence of a magnetic field is opened up, and a limit point is exposed. The onset of chaos is revealed in a dramatic way, and it is clear that detailed control by the external magnetic field can be exercised. The Lagrangian approach is adjusted to deal with dissipative systems, and through the choice of particular trial functions, aspects of the dynamic behavior of the spatial are predicted by this approach. Finally, some vortex dynamics in the Faraday configuration are investigated.