Born-Infeld 理论中阿贝尔 Higgs 模型畴壁解的存在性

Born-Infeld 理论中阿贝尔 Higgs 模型畴壁解的存在性

The Existence of Domain Wall Solution Arising in Abelian Higgs Model Subject to Born-Infeld Theory

摘要/Abstract

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (2): 567-575.

曹蕾¹(),陈筱^2,^*()

¹河南大学数学与统计学院河南开封 475004
²河南财经政法大学数学与信息科学学院郑州 450016

收稿日期:2024-04-25 修回日期:2024-12-23 出版日期:2025-04-26 发布日期:2025-04-09
通讯作者: 陈筱 E-mail:cllyhn@163.com;cx180910@163.com
作者简介:曹蕾，E-mail:cllyhn@163.com
基金资助:
国家自然科学基金(12101197);中国博士后科学基金(2022M721022)

Lei Cao¹(),Xiao Chen^2,^*()

¹School of Mathematics and Statistics, Henan University, Henan Kaifeng 475004
²School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450016

Received:2024-04-25 Revised:2024-12-23 Online:2025-04-26 Published:2025-04-09
Contact: Xiao Chen E-mail:cllyhn@163.com;cx180910@163.com
Supported by:
NSFC(12101197);China Postdoctoral Science Foundation(2022M721022)

摘要：

该文对出现在 Born-Infeld 理论中的 Ablelian Higgs 模型所对应的 BPS 方程, 针对两类边界条件, 利用动态射击法证明了 BPS 方程两点边值问题解的存在唯一性, 最后给出了解在无穷远处的渐近估计.

关键词: Born-Infeld 理论, 阿贝尔 Higgs 模型, 畴壁解, 动态射击法, 存在唯一性, 渐近估计

Abstract:

In this note, we research the Abelian Higgs model subject to the Born-Infeld theory for which the BPS equations can be reduced to a quasi-linear differential equation. We show that the equation exists a unique solution under two interesting boundary conditions which realize the corresponding phase transition. The solution is constructed using a dynamical shooting method for which the correct shooting slope is unique. We also obtain the sharp asymptotic estimate for the solution at infinity.

Key words: Born-Infeld theory, Abelian Higgs model, domain wall, dynamical shooting method, existence and uniqueness, asymptotic estimates

中图分类号:

O175.8

曹蕾,陈筱. Born-Infeld 理论中阿贝尔 Higgs 模型畴壁解的存在性[J]. 数学物理学报, 2025, 45(2): 567-575.

Lei Cao,Xiao Chen. The Existence of Domain Wall Solution Arising in Abelian Higgs Model Subject to Born-Infeld Theory[J]. Acta mathematica scientia,Series A, 2025, 45(2): 567-575.

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