  Weakly non-linear stability of regimes of free hydromagnetic thermal
convection in a rotating horizontal layer with free electrically conducting
boundaries is considered in the Boussinesq approximation. Perturbations are
supposed to involve large spatial and temporal scales. Applying methods for
homogenisation of parabolic equations, we derive the system of amplitude
equations governing the evolution of perturbations under the assumption that
the alpha-effect is insignificant in the leading order. The amplitude equations
involve the operators of anisotropic combined eddy diffusivity correction and
advection. The system is qualitatively different from the system of mean-field
equations for large-scale perturbations of forced convective hydromagnetic
regimes. It is mixed: equations for the mean magnetic perturbation are
evolutionary, all the rest involve neither time derivatives, nor the molecular
diffusivity operator.
