New non-radial solutions and concentration phenomena in the magnetic Ginzburg-Landau equations of superconductivity

超导磁金兹堡-朗道方程中的新非径向解和浓度现象

• 批准号: 298724-2012
• 负责人: Ting, Fridolin
• 金额: $ 0.87万
• 依托单位: Lakehead University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508523
• 关键词: New; non; radial; solutions; concentration

The proposed research will be on the magnetic Ginzburg-Landau equations on the whole plane and on bounded domains. These are coupled covariant nonlinear Schrodinger and Maxwell equations which describe (macroscopically) the behavior of superconductors at low and high temperatures and U(1) Higgs model of particle physics. I will find new non-radial magnetic vortex solutions to Ginzburg-Landau equations on the whole plane and vortex solutions concentrating on a subsets of bounded domains. The discovery of these new non-radial magnetic vortex solutions will give rise to questions on whether these configurations can be observed experimentally in superconductors. The analytical techniques used in finding these solutions will also generate ways to find other new solutions to other elliptic and non-linear partial differential equations. Therefore, this research will be of interest to both Physicists and Mathematicians. This work will explore the intimate relationship between elliptic partial differential equations, analysis and geometry.

本文拟研究全平面和有界域上的磁金兹堡-朗道方程。这些是耦合的协变非线性薛定谔和麦克斯韦方程，它们（宏观地）描述了超导体在低温和高温下的行为，以及粒子物理的U(1)希格斯模型。我将找到新的非径向磁涡解的金兹堡-朗道方程在整个平面和涡旋解集中在一个有界区域的子集。这些新的非径向磁涡旋解的发现将引起关于这些构型是否可以在超导体实验中观察到的问题。用于寻找这些解的解析技术也将产生寻找其他椭圆和非线性偏微分方程的其他新解的方法。因此，这项研究将引起物理学家和数学家的兴趣。这项工作将探讨椭圆偏微分方程，分析和几何之间的密切关系。