Applications of Darboux transformations to the self-dual Yang-Mills equations
type: Item
instance of: scholarly article
title: Applications of Darboux transformations to the self-dual Yang-Mills equations
zbMATH Open document ID: 0971.53022
DOI: 10.1007/BF02551200
published in: Theoretical and Mathematical Physics
publication date: 2000-11-23T00:00:00Z
review text: Solutions in closed form to the self-dual Yang-Mills equations are constructed in this paper by using Darboux transformations and binary Darboux transformations of almost classical type. The authors provide solutions of Wronskian-like and Gram-like determinants. The fact that binary Darboux transformations preserve the property that the associated Lax pair is self-adjoint for solutions in \(\mathrm{SU}(N)\) is used.
reviewed by: Jesús Hernández
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 37K35
zbMATH DE Number: 1535325
zbMATH Keywords: exact solution
zbMATH Keywords: self-dual Yang-Mills equations
zbMATH Keywords: Darboux transformation
zbMATH Keywords: Lax pair
author: J. J. C. Nimmo
author: Claire R. Gilson
author: Yasuhiro Ohta
MaRDI profile type: Publication
cites work: Instantons and algebraic geometry
cites work: Self-dual Yang-Mills fields over a sphere
cites work: Bilinear Form Approach to the Self-Dual Yang-Mills Equations and Integrable Systems in (2+1)-Dimension
cites work: The reduced self-dual Yang–Mills equation, binary and infinitesimal Darboux transformations
cites work: Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
description: scientific article; zbMATH DE number 1535325