Additional symmetries for integrable equations and conformal algebra representation
type: Item
instance of: scholarly article
title: Additional symmetries for integrable equations and conformal algebra representation
zbMATH Open document ID: 0618.35107
DOI: 10.1007/BF00416506
author: Yanyan Li
published in: Letters in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: We present a regular procedure for constructing an infinite set of additional (spacetime variables explicitly dependent) symmetries of integrable nonlinear evolution equations (INEEs). In our method, additional symmetry equations arise together with their L-A pairs, so that they are integrable themselves. This procedure is based on a modified 'dressing' method. For INEEs in \(1+1\) dimensions, some appropriate symmetry equations are shown to form the vector fields on a circle \(S^ 1\) algebra representation. In contrast to the so-called isospectral deformations, these symmetries result from conformal transformations of the associated linear problem spectrum. For INEEs in \(2+1\) dimensions, the commutation relations for symmetry equations are shown to coincide with operators \(\lambda^ m\partial_{\lambda}\), with integer m,p. Some additional results about Kac-Moody algebra applications are presented.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35G20
zbMATH DE Number: 4002691
zbMATH Keywords: symmetries
zbMATH Keywords: integrable nonlinear evolution equations
zbMATH Keywords: isospectral deformations
zbMATH Keywords: conformal transformations
zbMATH Keywords: associated linear problem spectrum
zbMATH Keywords: Kac-Moody algebra
MaRDI profile type: Publication
cites work: On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
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full work available at URL: https://doi.org/10.1007/bf00416506
OpenAlex ID: W2074767688
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description: scientific article; zbMATH DE number 4002691