Symmetries of Toda Equations

TL;DR

This paper investigates the symmetries of Toda equations, identifying a sequence of evolution vector fields and recursion operators that reveal the underlying algebraic structure and integrability properties.

Contribution

It introduces a new sequence of time-dependent evolution vector fields linked to master symmetries and constructs an infinite hierarchy of recursion operators for Toda equations.

Findings

Identification of a sequence of evolution vector fields with master symmetry components

Decomposition of master symmetries into group and Hamiltonian parts

Generation of an infinite sequence of recursion operators

Abstract

We find a sequence consisting of time dependent evolution vector fields whose time independent part corresponds to the master symmetries for the Toda equations. Each master symmetry decomposes as a sum consisting of a group symmetry and a Hamiltonian vector field. Taking Lie derivatives in the direction of these vector fields produces an infinite sequence of recursion operators.