Reduction and Realization in Toda and Volterra
Pantelis A. Damianou
TL;DR
This paper introduces a new symplectic, bi-hamiltonian realization of the KM-system derived from the Toda lattice, utilizing a reduction theorem, and reviews foundational work on these integrable systems.
Contribution
It presents a novel bi-hamiltonian realization of the KM-system through reduction techniques and revisits key developments in Toda and KM-systems.
Findings
New symplectic bi-hamiltonian structure for KM-system
Application of Fernandes and Vanhaecke's reduction theorem
Review of Moser's foundational work on Toda and KM-systems
Abstract
We construct a new symplectic, bi-hamiltonian realization of the KM-system by reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper we also review the important work of Moser on the Toda and KM-systems.
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