  Motivated by the difference between the dynamics of magnetization textures in
ferromagnets and antiferromagnets, the Landau-Lifshitz equation of motion is
explored. A typical one-dimensional domain wall in a bulk ferromagnet with
biaxial magnetic anisotropy is considered. In the framework of Walker-type of
solutions of steady-state ferromagnetic domain wall motion, the reduction of
the non-linear Landau-Lifshitz equation to a Lorentz-invariant sine-Gordon
equation typical for antiferromagnets is formally possible for velocities lower
than a critical velocity of the topological soliton. The velocity dependence of
the domain wall energy and the domain wall width are expressed in the
relativistic-like form in the limit of large ratio of the easy-plane/easy-axis
anisotropy constants. It is shown that the mapping of the Landau-Lifshitz
equation of motion to the sine-Gordon equation can be performed only by going
beyond the steady-motion Walker-type of solutions.
