  A parametrically forced sine-Gordon equation with a fast periodic {\em
mean-zero} forcing is considered. It is shown that $\pi$-kinks represent a
class of solitary-wave solutions of the equation. This result is applied to
quasi-one-dimensional ferromagnets with an easy plane anisotropy, in a rapidly
oscillating magnetic field. In this case the $\pi$-kink solution we have
introduced corresponds to the uniform ``true'' domain wall motion, since the
magnetization directions on opposite sides of the wall are anti-parallel. In
contrast to previous work, no additional anisotropy is required to obtain a
true domain wall. Numerical simulations showed good qualitative agreement with
the theory.
