Direct "Delay" Reductions of the Toda Equation
arXiv:0810.5581
Abstract
A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painlevé equations. The Lax pair associated to this equation is obtained, also by reduction.
To appear in FTC J.Phys. A; 8 pages