so(p,q) Toda Systems
arXiv:1205.3609 · doi:10.1016/j.physd.2013.01.001
Abstract
We define an integrable hamiltonian system of Toda type associated with the real Lie algebra $\so{p}{q}$. As usual there exists 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 type Toda lattice via a Flaschka type transformation. It is also obtained via a complex change of variables from the classical Toda lattice.
20 pages