Time-periodic N\'eel wall motions

In thin ferromagnetic films, the predominance of the magnetic shape anisotropy leads to in-plane magnetizations. The simplest domain wall in this geometry is the one-dimensional Neel wall that connects two magnetizations of opposite sign by a planar 180 degree rotation. In this paper, we perturb the static Neel wall profile in order to construct time-periodic Neel wall motions governed by to the Landau-Lifshitz-Gilbert equation. Our construction works within a certain parameter regime and requires the restriction to external magnetic fields with small amplitudes and suitable time averages.