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 with this equation is obtained, also by reduction.

PACS numbers: 02.30.Ik, 02.03.Ks

Mathematics Subject Classification: 37K10, 34K17

Print publication: Issue 2 (16 January 2009)
Received 7 September 2008, in final form 28 October 2008
Published 2 December 2008