New non-Noetherian Symmetries and Multi-Hamiltonian Structures for the Toda Lattice

TL;DR

This paper introduces new non-Noetherian symmetries for the Toda lattice, enabling the construction of multiple Lagrangian and Hamiltonian structures, and explores their algebraic properties.

Contribution

It presents novel symmetry transformations for the Toda lattice and derives associated multi-Hamiltonian structures, expanding the understanding of its geometric framework.

Findings

New symmetry transformations for the Toda lattice

Construction of multiple first order Lagrangian structures

Derivation of multi-Hamiltonian structures from Lagrangians

Abstract

New symmetry transformations for the n-dimensional Toda lattice are presented. Their existence allows for the construction of several first order Lagrangian structures associated to them. The multi-Hamiltonian structures are derived from Lagrangians in detail. The set of symmetries generates a Lie algebra.