  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 non-reciprocal behaviour 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 an opportunity is taken to display the
behaviour 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 action this leads to limit cycle plots that beautifully
reveal the behaviour 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 behaviour of the spatial are predicted by this approach.
Finally, some vortex dynamics in the Faraday configuration are investigated.
