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arXiv · 1603.04393

A symmetric difference-differential Lax pair for Painlevé VI

Christopher M. Ormerod·Eric M. Rains
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Abstract

We present a Lax pair for the sixth Painlevé equation arising as a continuous isomonodromic deformation of a system of linear difference equations with an additional symmetry structure. We call this a symmetric difference-differential Lax pair. We show how the discrete isomonodromic deformations of the associated linear problem gives us a discrete version of the fifth Painlevé equation. By considering degenerations we obtain symmetric difference-differential Lax pairs for the fifth Painlevé equation and the various degenerate versions of the third Painlevé equation.

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Christopher M. Ormerod, Eric M. Rains. 2016-12-21. A symmetric difference-differential Lax pair for Painlevé VI. https://arxiv.org/abs/1603.04393

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