The homogeneous realization of the basic representation of \(A_ 1^{(1)}\) and the Toda lattice
type: Item
instance of: scholarly article
title: The homogeneous realization of the basic representation of \(A_ 1^{(1)}\) and the Toda lattice
zbMATH Open document ID: 0614.17009
DOI: 10.1007/BF00416464
author: A. P. E. ten Kroode
author: Maarten Bergvelt
published in: Letters in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: The principal realization of the basic module \(L(\Lambda_ 0)\) over \(A_ 1(1)\) is known to give rise to the KdV hierarchy of partial differential equations. The authors use the homogeneous realization of the same module to construct a hierarchy of differential-difference equations, the first term of which turns out to be the equation for the Toda lattice. Thus, both hierarchies describe the same abstract orbit in \(L(\Lambda_ 0)\). In particular, the n-soliton solution of the KdV corresponds to a solution of the 2n-particle Toda lattice.
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 3993813
zbMATH Keywords: representation
zbMATH Keywords: affine Kac-Moody algebra
zbMATH Keywords: hierarchy of differential- difference equations
zbMATH Keywords: Toda lattice
zbMATH Keywords: n-soliton solution
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3993813