On the stability of static domain wall profiles in ferromagnetic thin film

In this article, we consider a two-dimensional model of ferromagnetic material. Our prime goal is to analyze the stability of static domain wall configuration calculated by Walker. The dynamics of magnetization inside the material is governed by the Landau–Lifschitz equation which is nonlinear and parabolic in nature. We prove the stability of the static waves solutions for the Landau–Lifschitz equation with a simplified expression of the stray field which is not unique in general, because of the non-convexity constraint |u| = 1.