An algebraic characterization of the bilinear relations of the matrix hierarchy associated with a commutative algebra of \(k\times k\)-matrices
type: Item
instance of: scholarly article
title: An algebraic characterization of the bilinear relations of the matrix hierarchy associated with a commutative algebra of \(k\times k\)-matrices
zbMATH Open document ID: 1194.35368
author: G. F. Helminck
author: Elena Panasenko
published in: Acta Applicandae Mathematicae
publication date: 2010-04-23T00:00:00Z
review text: A purely algebraic characterization for the equations of the matrix hierarchy that can be associated to a maximal commutative subalgebra of the \(k\times k\) matrices is presented. One starts with a description of the algebraic background of the corresponding system of equations and it is shown how they result from linearization. Then, the eigenfunctions occurring in this linear system are obtained. It is shown that these eigenfunctions, named wave functions, completely determine the solutions of the non-linear equations. One associates with them an eigenfunction -- the dual wave function -- and a characterization of the duality property is given. The algebraic framework used in this paper is adequate for the description of the linearization and the Lax form of the hierarchy. It is suggested that the results obtained allow an algebraic interpretation of the bilinear form of the respective system of nonlinear equations.
reviewed by: Gheorghe Zet
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 58B25
zbMATH DE Number: 5700578
zbMATH Keywords: matrix hierarchy
zbMATH Keywords: linearization
zbMATH Keywords: wavefunction
zbMATH Keywords: dual wavefunction
zbMATH Keywords: bilinear relations
MaRDI profile type: Publication
full work available at URL: s10440-009-9440-6
OpenAlex ID: W2094354500
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DOI: 10.1007/S10440-009-9440-6
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description: scientific article; zbMATH DE number 5700578