一类耦合Ginzburg-Landau系统的局部极小解

数学物理学报 ›› 2023, Vol. 43 ›› Issue (2): 321-340.

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一类耦合Ginzburg-Landau系统的局部极小解

熊晨(),高琦^*()

武汉理工大学理学院数学系武汉 430070

收稿日期:2022-08-26 修回日期:2023-02-06 出版日期:2023-04-26 发布日期:2023-04-17
通讯作者: 高琦，E-mail: gaoq@whut.edu.cn
作者简介:熊晨，E-mail: 924821516@qq.com
基金资助:
国家自然科学基金(11931012);国家自然科学基金(11871386);中央高校基本科研业务费专项基金(2020IB019)

Locally Minimizing Solutions of a Two-component Ginzburg-Landau System

Xiong Chen(),Gao Qi()

Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070

Received:2022-08-26 Revised:2023-02-06 Online:2023-04-26 Published:2023-04-17
Supported by:
NSFC(11931012);NSFC(11871386);Fundamental Research Funds for the Central Universities(2020IB019)

摘要/Abstract

摘要：

该文考虑耦合Ginzburg-Landau系统整体解中一类特殊的解-局部极小解的相关性质,证明了局部极小解的环绕度一定是$n_\pm \in \{0,\pm1\}$. 同时, 该文还证明了局部极小解的两个分量中其中一个为零, 而另一个不为零, 即物理中的少核涡旋现象.

关键词: 椭圆方程组, 局部极小解, 变分法

Abstract:

In this paper, we consider a Ginzburg-Landau functional for a complex vector order parameter $\Psi=[\psi_+, \psi_-]$. In particular, we consider entire solutions in all ${\Bbb R}^2$, which are obtained by blowing up around vortices. Among the entire solutions we distinguish those which are locally minimizing solutions, and we show that locally minimizing solutions must have degrees $n_\pm \in \{0, \pm1\}$. By studying the local structure of these solutions, we also show that one component of the solution vanishes, but the other does not, which describes the coreless vortex phenomenon in physics.

Key words: Elliptic systems, Locally minimizing solutions, Variational methods for elliptic systems

中图分类号:

O175.2

熊晨, 高琦. 一类耦合Ginzburg-Landau系统的局部极小解[J]. 数学物理学报, 2023, 43(2): 321-340.

Xiong Chen, Gao Qi. Locally Minimizing Solutions of a Two-component Ginzburg-Landau System[J]. Acta mathematica scientia,Series A, 2023, 43(2): 321-340.

参考文献 14

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一类耦合Ginzburg-Landau系统的局部极小解

Locally Minimizing Solutions of a Two-component Ginzburg-Landau System

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