  A wide class of models, built of the three component unit vector field living
in the (3+1) Minkowski space-time, which break explicitly global O(3) symmetry
are discussed. The symmetry breaking occurs due to the so-called dielectric
function multiplying a standard symmetric term. Integrability conditions are
found. Moreover, for some particular forms of the Lagrangian exact toroidal
solutions with any Hopf index are obtained. It is proved that such symmetry
breaking influences the shape of the solitons whereas the energy as well as the
Hopf index remain unchanged.
