Direct "Delay" Reductions of the Toda Equation and Hierarchy
by
Nalini Joshi
School of Mathematics and Statistics, The University of Sydney, NSW 2006 Australia
Coauthors: Paul E. Spicer

A new direct method of obtaining reductions of the Toda equation and its hierarchy 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.

Date received: January 12, 2010