﻿ Landau-Lifshitz方程的Fourier展开 The Fourier Expansion of Landau-Lifshitz Equations

Advances in Applied Mathematics
Vol.06 No.01(2017), Article ID:19587,8 pages
10.12677/AAM.2017.61004

The Fourier Expansion of Landau-Lifshitz Equations

Liyuan Ding, Peng Zhu

College of Mathematics, Yunnan Normal University, Kunming Yunnan

Received: Jan. 1st, 2017; accepted: Jan. 17th, 2017; published: Jan. 22nd, 2017

Copyright © 2017 by authors and Hans Publishers Inc.

ABSTRACT

Landau-Lifshitz equations describes magnetic phenomena of magnetization dynamics equation; studying the material is very meaningful. Scholars have constructed some explicit solutions. In this paper, we study the Landau-Lifshitz equations, which have no external magnetic field and the dissipation term is zero, by Fourier expansion. And we also give the iterative relations of finite terms of the equation.

Keywords:Landau-Lifshitz Equations, Fourier Expansion, Integral, Iteration

Landau-Lifshitz方程的 Fourier展开

Landau-Lifshitz方程是描述磁性物质动态磁化现象的方程，而研究磁性物质是非常有意义的。目前学者们构造了部分精确解，本文利用Fourier展开研究无外加磁场且耗散项为零时的Landau-Lifshitz方程，给出方程有限项的迭代关系。

1. 引言

1935年，Landau和Lifshitz在研究铁磁体的磁导率时，给出了如下的磁化运动方程 [1] [2] ：

2. 对Landau-Lifshitz方程的常微分求解

3. Landau-Lifshitz方程的Fourier展开

3.1. 通过计算

3.2. 两边与做点乘后，在上分别积分

3.3. 两边与做点乘后，在上分别积分

3.4. 有限项的Landau-Lifshitz方程

The Fourier Expansion of Landau-Lifshitz Equations[J]. 应用数学进展, 2017, 06(01): 29-36. http://dx.doi.org/10.12677/AAM.2017.61004

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