Existence of travelling-wave solutions representing domain wall motion in a thin ferromagnetic nanowire

TL;DR

This paper proves the existence of travelling-wave solutions representing domain wall motion in a thin ferromagnetic nanowire, using mathematical analysis of the Landau--Lifshitz--Gilbert equation.

Contribution

It establishes the existence of travelling-wave solutions near static solutions in a ferromagnetic nanowire, advancing understanding of magnetic domain dynamics.

Findings

Existence of travelling-wave solutions proven mathematically.

Solutions are close to known static solutions.

Analysis uses implicit-function-theorem-type arguments.

Abstract

We study the dynamics of a domain wall under the influence of applied magnetic fields in a one-dimensional ferromagnetic nanowire, governed by the Landau--Lifshitz--Gilbert equation. Existence of travelling-wave solutions close to two known static solutions is proven using implicit-function-theorem-type arguments.