  Directed motion of domain walls (DWs) in a classical biaxial ferromagnet
placed under the influence of periodic unbiased external magnetic fields is
investigated. Using the symmetry approach developed in this article the
necessary conditions for the directed DW motion are found. This motion turns
out to be possible if the magnetic field is applied along the most easy axis.
The symmetry approach prohibits the directed DW motion if the magnetic field is
applied along any of the hard axes. With the help of the soliton perturbation
theory and numerical simulations, the average DW velocity as a function of
different system parameters such as damping constant, amplitude, and frequency
of the external field, is computed.
