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

Part of: Partial differential equations Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  17 October 2017

Ross G. Lund ,
J. M. Robbins  and
Valeriy Slastikov
Ross G. Lund
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
J. M. Robbins
Affiliation:
University of Bristol School of Mathematics, University Walk, Bristol BS8 1TW, UK (valeriy.slastikov@bristol.ac.uk)
Valeriy Slastikov
Affiliation:
University of Bristol School of Mathematics, University Walk, Bristol BS8 1TW, UK (valeriy.slastikov@bristol.ac.uk)
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Abstract

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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.

Keywords

Landau–Lifshitz–Gilbert equationsmagnetic domain wallstravelling wavesexistence of solutions

MSC classification

Secondary: 35A01: Existence problems 35Q60: PDEs in connection with optics and electromagnetic theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 2 , April 2018 , pp. 395 - 407
Copyright
Copyright © Royal Society of Edinburgh 2018