On the Integrability of the Toda Lattice

Abstract

This paper presents a variety of computer generated evidence indicating that the Toda lattice behaves remarkably like an integrable, nonlinear system, where here integrability means that the system Hamiltonian can be brought to an obviously integrable form. In particular, we investigate Toda lattices having three and six particles, using periodic boundary conditions. While computer calculations cannot rigorously prove integrability, the evidence presented here is sufficiently strong to provide incentive for seeking the general, closed form, analytic solution or, at least, some approximation to it.