Toda systems

We define an integrable Hamiltonian system of Toda type associated with the real Lie algebra s o ( p , q ) . As usual there exist a periodic and a non-periodic version. We construct, using the root space, two Lax pair representations and the associated Poisson tensors. We prove Liouville integrability and examine the multi-Hamiltonian structure. The system is a projection of a canonical A n type Toda lattice via a Flaschka transformation. It is also obtained via a complex change of variables from the classical Toda lattice.