The finite Toda lattices
type: Item
instance of: scholarly article
title: The finite Toda lattices
zbMATH Open document ID: 0677.35086
DOI: 10.1007/BF01218159
author: V. I. Inozemtsev
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: A potentially fruitful field of research is opened by this paper in which the author uses his previous results that multiparticle systems in which the structure of an interaction potential is defined by the systems of all positive, and not just simple roots of classical Lie algebras are also completely integrable. Flaschka and Moser have proved complete integrability of finite dimensional Hamiltonian systems of that kind (nonperiodic and periodic Toda lattices). Kostant, Olshanetsky and Perelomov have established the connection between nonperiodic lattices and Lie algebras. The author also shows that the above-listed Toda lattices are particular cases of these systems corresponding to certain limit situations. And taking advantage of that correspondence, the author succeeded in obtaining new integrable lattices differing from the known ones by the interaction of particles near the ends. Explicit expressions for the Lax matrices of the new lattices and non-Abelian generalization of some of them are presented at the end of the paper. They are too complicated to reproduce them here.
reviewed by: F. M. Ragab
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 17B65
zbMATH DE Number: 4109268
zbMATH Keywords: Kac-Moody algebras
zbMATH Keywords: Lax representation
zbMATH Keywords: spectral parameter
zbMATH Keywords: multiparticle systems
zbMATH Keywords: interaction potential
zbMATH Keywords: Lie algebras
zbMATH Keywords: completely integrable
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Toda lattices
zbMATH Keywords: nonperiodic lattices
zbMATH Keywords: integrable lattices
zbMATH Keywords: interaction of particles
zbMATH Keywords: Explicit expressions
zbMATH Keywords: Lax matrices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4109268