\(N\)-soliton-type solutions of the self-dual Yang-Mills equations in \(M^ 4\)
type: Item
instance of: scholarly article
title: \(N\)-soliton-type solutions of the self-dual Yang-Mills equations in \(M^ 4\)
zbMATH Open document ID: 0851.53015
DOI: 10.1007/BF01016133
author: R. K. Bullough
author: B. S. Getmanov
author: Paul Sutcliffe
published in: Theoretical and Mathematical Physics
publication date: 1996-11-10T00:00:00Z
review text: The purpose of this paper is to study the \(N\)-soliton-type solutions of the self-dual Yang-Mills (sdYM) equations in \(M^4\), and the case \(N = 2\) by using computers. The authors discuss the sdYM equations in Minkowski spacetime \(M^4\), \[ F_{\mu \nu} = {1\over 2} i \varepsilon_{\mu v \alpha \beta} F^{\alpha \beta} \tag{1} \] where \[ F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu + [A_\mu, A_\nu] \tag{2} \] and \(\varepsilon_{\mu \nu \alpha \beta}\) is the totally antisymmetric 4-tensor. They present two ways of obtaining exact \(N\)-soliton-type solutions of equations (1) and (2), construct a regular spherically symmetric one-soliton-type solution of (1), and give a corresponding \(N\)-soliton-type generalization.
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 35Q51
zbMATH DE Number: 907299
zbMATH Keywords: self-dual Yang-Mills equations
zbMATH Keywords: four-manifold
zbMATH Keywords: spherically symmetric solutions
zbMATH Keywords: Minkowski space-time
zbMATH Keywords: exact \(N\)-soliton-type solutions
MaRDI profile type: Publication
cites work: Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
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description: scientific article; zbMATH DE number 907299