In this paper, the nonlinear (orbital) stability of static 180^\circ N\'eel walls in ferromagnetic films, under the reduced wave-type dynamics for the in-plane magnetization proposed by Capella, Melcher and Otto [CMO07], is established. It is proved that the spectrum of the linearized operator around the static N\'eel wall lies in the stable complex half plane with non-positive real part. This information is used to show that small perturbations of the static N\'eel wall converge to a translated orbit belonging to the manifold generated by the static wall.
@article{arxiv.2309.04432,
title = {Nonlinear Stability of Static N\'eel Walls in Ferromagnetic Thin Films},
author = {A. Capella and C. Melcher and L. Morales and R. G. Plaza},
journal= {arXiv preprint arXiv:2309.04432},
year = {2024}
}