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.
- Pub Date:
- January 2000
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- High Energy Physics - Theory;
- Mathematics - Algebraic Geometry;
- Mathematics - Analysis of PDEs
- LaTeX2e,18 pages, 3 postscript figures, submitted to Glasgow Mathematical Journal Trust for Island I proceedinds