The Discrete and Continuous Painleve VI Hierarchy and the Garnier Systems

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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.
LaTeX2e,18 pages, 3 postscript figures, submitted to Glasgow Mathematical Journal Trust for Island I proceedinds

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Exactly Solvable and Integrable Systems, High Energy Physics - Theory, Algebraic Geometry, Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/79725

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0001054
 http://arxiv.org/abs/nlin/0001054

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arXiv