The discrete and continuous Painlevé VI hierarchy and the Garnier systems
By F. Nijhoff, Alan J. Walker. Glasgow Mathematical Journal, 2000
224 citations recorded by the source corpus.
We present a general scheme to derive higher-order members of the Painlevé 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.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/874a236434488300034975005560d6b398499ac1
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In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Lax pair for the Adler (lattice Krichever–Novikov) system (2001, methodology): “[21] for details, (in the paper [14] we gave the lattice modified KdV equation as an example, where the scheme works precisely in the same way).”
- Symmetries of Integrable Difference Equations on the Quad‐Graph (2007, unknown): “Five-point symmetries for H1, H3δ=0 and Q1δ=0 have already appeared in [4, 10, 20, 21, 22, 23, 24, 25, 27, 33, 34].”
- Soliton solutions for ABS lattice equations: I. Cauchy matrix approach (2009, background): “[24, 11], where p and q play the role of lattice parameters.”