Reduction of the symmetries of the self-dual Yang-Mills equation
type: Item
instance of: scholarly article
title: Reduction of the symmetries of the self-dual Yang-Mills equation
zbMATH Open document ID: 0791.35116
published in: Chinese Science Bulletin
publication date: 1994-07-18T00:00:00Z
review text: We know that the self-dual Yang-Mills (SDYM) equation has infinitely many symmetries, and these symmetries constitute an infinite dimensional Lie algebra. This property is commonly shared by almost all the \(1+1\)- dimensional integrable evolution equations (soliton equations), and has become a very important criterion of integrability for the evolution equations. So in a sense the SDYM equation is integrable. In recent years people have found that some typical soliton equations, such as the KdV equation, the nonlinear Schrödinger (NLS) equation and the Toda lattice equation, can be reduced from the SDYM equation. In this note we show that the symmetries and their Lie algebraic structure of the above-mentioned soliton equations can be reduced from those of the SDYM equation. Since the symmetries of the above-mentioned soliton equations correspond to some isospectral and non-isospectral hierarchies of soliton equations, we thus build more relations between the SDYM equation and the soliton equations.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 558934
zbMATH Keywords: soliton equations
zbMATH Keywords: symmetries
zbMATH Keywords: Lie algebraic structure
author: Youjin Zhang
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 558934