Some explicit solutions of the Landau-Lifshitz equation for anisotropic ferromagnets

被引：2

作者：

Han, Fangyu ^{[1
]}

Yang, Ganshan ^{[1
,2
]}

机构：

[1] Yunnan Minzu Univ, Dept Math, Kunming 650504, Yunnan, Peoples R China

[2] Yunnan Normal Univ, Inst Math, Kunming, Yunnan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 17期

基金：

美国国家科学基金会;

关键词：

anisotropic ferromagnets; explicit solution; higher-order approximations; Landau-Lifshitz equation; the cubic system; DYNAMICS; MODEL;

D O I：

10.1002/mma.5246

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to construct explicit solutions of the Landau-Lifshitz equation for anisotropic ferromagnets. Firstly, we present some explicit solutions for n-dimensional Landau-Lifshitz equation with a generalized uniaxial anisotropy field (depending only on time) under a suitable transformation, where the generalized uniaxial anisotropy field contains the classical easy-axis case and the important higher-order approximations. Some relevant examples are indicated that contains the cubic system proposed by Landau and Lifshitz in 1960. Secondly, an explicit plane-wave solution of Landau-Lifshitz equation for the completely anisotropic case is obtained. Finally, some properties of magnetization for ferromagnets are provided by analysis of the solutions.

引用

页码：7839 / 7851

页数：13

共 22 条

[1]

Aharoni A., 2000, Introduction to the Theory of Ferromagnetism

[2]

[Anonymous], 2000, COMMUN NONLINEAR SCI

[3]

[Anonymous], 2008, Landau-Lifshitz Equations

[4]

[Anonymous], 2001, ADV MATH

[5]

[Anonymous], LANDAU LIFSHITZ EQUA

[6]

[Anonymous], HAMILTONIAN METHODS

[7]

Bakhvalov N. S., 1987, Numerical Methods

[8] Landau-Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions [J].

Bikbaev, R. F. ;

Bobenko, A. I. ;

Its, A. R. .

THEORETICAL AND MATHEMATICAL PHYSICS, 2014, 178 (02) :143-193

[9]

BOGDAN MM, 1980, JETP LETT+, V31, P424

[10] Stability in the energy space for chains of solitons of the Landau-Lifshitz equation [J].

de Laire, Andre ;

Gravejat, Philippe .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 258 (01) :1-80

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