Separability of the Toda Lattice Original Research Article

We study integrability of the nonperiodic, finite-dimensional Toda Lattice (TL) from the point of view of the Hamilton-Jacobi (HJ) theory of separation of variables. Known to be completely integrable in the sense of Arnolʹd-Liouville, the system nonetheless cannot be integrated by the HJ method in the ‘original’ generalized physical position-momenta coordinates. The intrinsic (coordinate-free) characterization method by Benenti provides a tool to investigate the separability of the TL system independently of a local system of coordinates.