  Parametrically excited sine-Gordon equation is considered. Excitation is a
fast oscillating periodic function with zero mean. Technique of classical
method of averaging enables to construct the averaged equations in a variety of
assumptions about driving amplitude. The averaged equation possesses kinks
solutions. The results can be applied to the study of movement of Bloch walls
for ferromagnetic crystals in the presence of a rapidly oscillating magnetic
field and to describe the fluxon dynamics in long Josephson junctions.
