Direct "Delay" Reductions of the Toda Equation

Details Direct "Delay" Reductions of the Toda Equation Direct "Delay" Reductions of the Toda Equation

2008-10-30

arxiv.org/abs/0810.5581v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

To appear in FTC J.Phys. A; 8 pages

Scientific paper

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 Painlev\'e equations. The Lax pair associated to this equation is obtained, also by reduction.

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