The Discrete and Continuous Painleve VI Hierarchy and the Garnier Systems
Exactly Solvable and Integrable Systems
2007-05-23 v1 High Energy Physics - Theory
Algebraic Geometry
Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.nlin/0001054,
title = {The Discrete and Continuous Painleve VI Hierarchy and the Garnier Systems},
author = {F. W. Nijhoff and A. J. Walker},
journal= {arXiv preprint arXiv:nlin/0001054},
year = {2007}
}
Comments
LaTeX2e,18 pages, 3 postscript figures, submitted to Glasgow Mathematical Journal Trust for Island I proceedinds