A class of Liouville-integrable Hamiltonian systems with two degrees of freedom

A class of two-dimensional Liouville-integrable Hamiltonian systems is studied. Separability of the corresponding Hamilton-Jacobi equation for these systems is shown to be equivalent to other fundamental properties of Hamiltonian systems, such as the existence of the Lax and bi-Hamiltonian representations of certain fixed types. Applications to physical models, including the Calogero-Moser model, an integrable case of the Henon-Heiles potential and the nonperiodic Toda lattice are presented. (C) 2000 American Institute of Physics. [S0022-2488(00)01110-5].