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math-ph2026
A Tau function for -Painlevé VI as a Fredholm determinant
Harini Desiraju, Pieter Roffelsen
We give an analytic construction of a tau function for the -difference sixth Painlevé equation (PVI) as a Fredholm determinant through the general Riemann-Hilbert problem ass…
nlin.SI2026
On difference-differential Lax pairs and integrals of Painlevé equations in finite characteristic
Nalini Joshi, Tomas Lasic Latimer, Pieter Roffelsen
We collect rank two difference-differential Lax pairs for classical Painlevé equations in the literature and put each in matrix form with the coefficient matrix of the…
nlin.SI2026
On integrals of non-autonomous dynamical systems in finite characteristic
Nalini Joshi, Pieter Roffelsen
We use a difference Lax form to construct simultaneous integrals of motion of the fourth Painlevé equation and the difference second Painlevé equation over fields with finite chara…