Solitons of the two-dimensional 3-component gauged sigma model
type: Item
instance of: scholarly article
title: Solitons of the two-dimensional 3-component gauged sigma model
zbMATH Open document ID: 0922.34023
author: Shangbing Ai
author: Xinfu Chen
published in: Journal of Differential Equations
publication date: 1999-10-14T00:00:00Z
review text: The paper deals with the following boundary value problem arising from field theory (P): \[ u''+{1\over r} u'-\left({m^2(1-v)^2 \over r^2}+p \right)\sin u\cos u=0\text{ for }r>0, \] \[ v''-{1\over r} v'+2(1-v) \sin^2u=0 \text{ for }r>0, \] \[ u(0)= v(0)=v'(\infty)=0,\;u(\infty)=\pi,\quad u'>0,\;v'>0,\;v<1\text{ for }r>0. \] The main result is the following theorem: 1) For every \(m>0\), if \(p\geq 4m\), there is no solution to \((P)\). 2) For every \(m>0\), there exists \(p^*=p^* (m)>0\) such that for every \(p\in(0,p^*)\), there exists at least one solution to \((P)\). In addition, when \(m>1\), a lower bound for \(p^*(m)\) is given. The existence part of the theorem is proved by a shooting argument.
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1278766
zbMATH Keywords: solitons
zbMATH Keywords: two-dimensional 3-component
zbMATH Keywords: gauged sigma model
zbMATH Keywords: field theory
reviewed by: Radu Precup
MaRDI profile type: Publication
OpenAlex ID: W2035256364
cites work: Q3467253
cites work: The existence of similar solutions for some laminar boundary layer problems
cites work: Q4059363
DOI: 10.1006/JDEQ.1998.3544
description: scientific article; zbMATH DE number 1278766