Master symmetries and r-matrices for the Toda lattice
type: Item
instance of: scholarly article
title: Master symmetries and r-matrices for the Toda lattice
zbMATH Open document ID: 0714.70014
DOI: 10.1007/BF00398275
author: Pantelis A. Damianou
published in: Letters in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: The Toda lattice is the Hamiltonian mechanical system \(({\mathbb{R}}^{2n}\), \(\sum^{N}_{i=1}dp_ i\wedge dq^ i\), \(H=\sum^{N}_{i=1}p^ 2_ i+\sum^{N}_{i=1}e^{q^ i-q^ i+1})\) with \(q^ 0=q^{N+1}=0\). This system is completely integrable via the well known Flaschka's transformation with respect to a linear Poisson bracket \(w_ 1.\) In the paper under review the author constructs in a very ingeniuous manner a sequence of Poisson brackets \((W_ n)_{n\in {\mathbb{N}}}\) such that respect to each of them the Toda lattice remains a completely integrable mechanical system, and also points out some of their properties.
reviewed by: Mircea Puta
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82C20
zbMATH DE Number: 4176528
zbMATH Keywords: Toda lattice
zbMATH Keywords: Hamiltonian mechanical system
zbMATH Keywords: completely integrable
zbMATH Keywords: Flaschka's transformation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4176528