Direct "Delay" Reductions of the Toda Equation

Nalini Joshi

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arXiv · 0810.5581

Direct "Delay" Reductions of the Toda Equation

Nalini Joshi

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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.

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Nalini Joshi. 2008-10-30. Direct "Delay" Reductions of the Toda Equation. https://arxiv.org/abs/0810.5581

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