An elegant solution of the n-body Toda problem

TL;DR

This paper presents a novel, symmetric solution to the classical open-chain n-body Toda problem, utilizing an ansatz and Vandermonde determinant identities, and provides an explicit transformation to action-angle variables.

Contribution

It introduces a new symmetric solution approach for the n-body Toda problem and explicitly derives the transformation to action-angle variables.

Findings

Solution derived from an ansatz with high symmetry

Proof involves Vandermonde determinant identities

Explicit action-angle transformation provided

Abstract

The solution of the classical open-chain n-body Toda problem is derived from an ansatz and is found to have a highly symmetric form. The proof requires an unusual identity involving Vandermonde determinants. The explicit transformation to action-angle variables is exhibited.