Landau-Lifshitz方程的Fourier展开
The Fourier Expansion of Landau-Lifshitz Equations
DOI: 10.12677/AAM.2017.61004, PDF, HTML, XML, 下载: 1,558  浏览: 2,211 
作者: 丁莉园, 朱鹏：云南师范大学数学学院，云南 昆明
关键词: Landau-Lifshitz方程；Fourier展开；积分；迭代格式；Landau-Lifshitz Equations； Fourier Expansion； Integral； Iteration
摘要: 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。
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.
文章引用：丁莉园, 朱鹏. Landau-Lifshitz方程的Fourier展开[J]. 应用数学进展, 2017, 6(1): 29-36. http://dx.doi.org/10.12677/AAM.2017.61004

参考文献

[1] 杨干山. 多维Landau-Lifshitz方程的型黏性解、Blow up解和整体解[D]: [博士学位论文]. 北京: 中国工程物理研究院, 2002: 1-11.
[2] 郭柏灵, 丁时进. 自旋波与铁磁链方程[M]. 浙江: 浙江科学技术出版社, 2002: 1-12.
[3] Guo, B. and Yang, G.S. (2001) Some Exact Nontrivial Global Solutions with Values in Unit Sphere for Two-Dimen- sional Landau-Lifshitz Equations. Journal of Mathematical Physics, 42, 5223-5227.
https://doi.org/10.1063/1.1402955
[4] Guo, B., Han, Y.Q. and Yang, G. S. (2001) Exact Blow-Up Solutions for Mul-tidimensional Landau-Lifshitz Equations. Advances in mathematics (China), 30, 91-93.
[5] 刘利敏. Landau-Lifshitz方程解的一些研究[D]: [博士学位论文]. 重庆: 重庆大学, 2010.
[6] Vretblad, A. Fourier Analysis and Its Appli-cations. 北京: 北京科学技术出版社, 2002: 1-12.

为你推荐