On planar selfdual electroweak vortices
type: Item
instance of: scholarly article
title: On planar selfdual electroweak vortices
zbMATH Open document ID: 1073.35079
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2004-11-23T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78615
review text: The authors deal with the analysis of self-dual electroweak vortices that can be reduced to the study of the following elliptic system \[ \begin{aligned} -\Delta u_1&= 4g^2 e^{u_1}+ g^2 e^{u_2}- 4\pi \sum^m_{k=1} n_k\delta(z- z_k),\\ \Delta u_2&= {g^2\over 2\cos^2\theta} (e^{u_2}- \varphi^2_0)+ 2g^2 e^{u_1},\end{aligned}\tag{1} \] where \(\varphi_0\) is a given positive parameter, \(g\) is the \(\text{SU}(2)\)-coupling constant, and \(\theta\in (0,{\pi\over 2})\) is the so-called ``Weinberg angle'', related with the \(U(1)\)-coupling constant \(g_*\) via the relation \(\cos\theta= {g\over (g^2+ g^2_*)^{1/2}}\). The authors mainly interested in planar vortex-type configurations, and consider (1) over \(\mathbb{R}^2\) subject to appropriate decay assumptions at infinity.
Mathematics Subject Classification ID: 35J45
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 37K40
Mathematics Subject Classification ID: 70S15
zbMATH DE Number: 2117901
zbMATH Keywords: vortex-solution
zbMATH Keywords: elliptic systems
author: Dongho Chae
author: G. Tarantello
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2076984541
cites work: Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory
cites work: Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)euin two dimensions
cites work: The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory
cites work: Qualitative properties of solutions to some nonlinear elliptic equations in \(\mathbb{R}^2\)
cites work: On a class of elliptic problems in \(\mathbb{R}^2\): Symmetry and uniqueness results
cites work: On multivortices in the electroweak theory. I: Existence of periodic solutions
cites work: On multivortices in the electroweak theory. II: Existence of Bogomol'nyi solutions in \(\mathbb R^2\)
cites work: Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations
cites work: On the equivalence of the first and second order equations for gauge theories
cites work: Q2734533
DOI: 10.1016/J.ANIHPC.2003.01.001
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description: scientific article; zbMATH DE number 2117901