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The Discrete and Continuous Painleve VI Hierarchy and the Garnier Systems

F. W. Nijhoff·A. J. Walker
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Abstract

We present a general scheme to derive higher-order members of the Painleve VI (PVI) hierarchy of ODE's as well as their difference analogues. The derivation is based on a discrete structure that sits on the background of the PVI equation and that consists of a system of partial difference equations on a multidimensional lattice. The connection with the isomonodromic Garnier systems is discussed.

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F. W. Nijhoff, A. J. Walker. 2000-01-25. The Discrete and Continuous Painleve VI Hierarchy and the Garnier Systems. https://arxiv.org/abs/nlin/0001054

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