Parametrically forced sine-Gordon equation and domain wall dynamics in ferromagnets

A parametrically forced sine-Gordon equation with a fast periodic mean-zero forcing is considered. It is shown that $\ensuremath{\pi}$ 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 $\ensuremath{\pi}$-kink solution we have introduced corresponds to the uniform ``true'' domain-wall motion, since the magnetization directions on opposite sides of the wall are antiparallel. 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.

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