Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation

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Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation. / Gutierrez, Susana; De Laire, Andre .

In: Nonlinearity, Vol. 28, No. 5, 17.04.2015, p. 1307-1350.

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@article{157ae42022544f0a9158fa871fc2906f,
title = "Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation",
abstract = "We consider the one-dimensional Landau-Lifshitz-Gilbert (LLG) equation, a model describing the dynamics for the spin in ferromagnetic materials. Our main aim is the analytical study of the bi-parametric family of self-similar solutions of this model. In the presence of damping, our construction provides a family of global solutions of the LLG equation which are associated with discontinuous initial data of infinite (total) energy, and which are smooth and have finite energy for all positive times. Special emphasis will be given to the behaviour of this family of solutions with respect to the Gilbert damping parameter.We would like to emphasize that our analysis also includes the study of self-similar solutions of the Schr{\"o}dinger map and the heat flow for harmonic maps into the 2-sphere as special cases. In particular, the results presented here recover some of the previously known results in the setting of the 1D-Schr{\"o}dinger map equation.",
keywords = "Landau–Lifshitz–Gilbert equation, ferromagnetic spin chain, Schrodinger maps, heat-flow for harmonic maps, self-similar solutions, asymptotics",
author = "Susana Gutierrez and {De Laire}, Andre",
year = "2015",
month = apr,
day = "17",
doi = "10.1088/0951-7715/28/5/1307",
language = "English",
volume = "28",
pages = "1307--1350",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing",
number = "5",

}

RIS

TY - JOUR

T1 - Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation

AU - Gutierrez, Susana

AU - De Laire, Andre

PY - 2015/4/17

Y1 - 2015/4/17

N2 - We consider the one-dimensional Landau-Lifshitz-Gilbert (LLG) equation, a model describing the dynamics for the spin in ferromagnetic materials. Our main aim is the analytical study of the bi-parametric family of self-similar solutions of this model. In the presence of damping, our construction provides a family of global solutions of the LLG equation which are associated with discontinuous initial data of infinite (total) energy, and which are smooth and have finite energy for all positive times. Special emphasis will be given to the behaviour of this family of solutions with respect to the Gilbert damping parameter.We would like to emphasize that our analysis also includes the study of self-similar solutions of the Schrödinger map and the heat flow for harmonic maps into the 2-sphere as special cases. In particular, the results presented here recover some of the previously known results in the setting of the 1D-Schrödinger map equation.

AB - We consider the one-dimensional Landau-Lifshitz-Gilbert (LLG) equation, a model describing the dynamics for the spin in ferromagnetic materials. Our main aim is the analytical study of the bi-parametric family of self-similar solutions of this model. In the presence of damping, our construction provides a family of global solutions of the LLG equation which are associated with discontinuous initial data of infinite (total) energy, and which are smooth and have finite energy for all positive times. Special emphasis will be given to the behaviour of this family of solutions with respect to the Gilbert damping parameter.We would like to emphasize that our analysis also includes the study of self-similar solutions of the Schrödinger map and the heat flow for harmonic maps into the 2-sphere as special cases. In particular, the results presented here recover some of the previously known results in the setting of the 1D-Schrödinger map equation.

KW - Landau–Lifshitz–Gilbert equation

KW - ferromagnetic spin chain

KW - Schrodinger maps

KW - heat-flow for harmonic maps

KW - self-similar solutions

KW - asymptotics

U2 - 10.1088/0951-7715/28/5/1307

DO - 10.1088/0951-7715/28/5/1307

M3 - Article

VL - 28

SP - 1307

EP - 1350

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 5

ER -