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The negative Toda hierarchy and rational Poisson brackets

✍ Scribed by Pantelis A. Damianou

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 135 KB
Volume: 45
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(02)00137-7

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✦ Synopsis

In this paper we extend the usual hierarchies for the finite, nonperiodic Toda lattice for negative values of the index. We define an infinite sequence of rational homogeneous Poisson brackets, master symmetries, invariants and investigate the various relationships between them. All the relations between master symmetries, Poisson tensors and invariants which hold over the positive integers are extended for all integer values. We comment on extensions to other versions of the Toda lattice, i.e. the periodic, infinite and Bogoyavlensky-Toda type systems.

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