So (p, q) Toda systems

Abstract

We define an integrable Hamiltonian system of Toda type associated with the real Lie algebra so(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 An type Toda lattice via a Flaschka transformation. It is also obtained via a complex change of variables from the classical Toda lattice.© 2013 Elsevier B.V. All rights reserved.