Separability of the Toda Lattice

We study integrability of the nonperiodic, finite-dimensional Toda Lattice (TL) from the point of view of the Hamilton-Jacobi (HJ) theory of separatio n of variables. Known to be completely integrable in the sense of Amol'd-Li ouville, the system nonetheless cannot be integrated by the HJ method in th e 'original' generalized physical position-momenta coordinates. The intrins ic (coordinate-free) characterization method by Benenti provides a tool to investigate the separability of the TL system independently of a local syst em of coordinates. (C) 2000 Elsevier Science Ltd. All rights reserved.