Geodesic
Quantum Painlevé Equations: from Continuous to Discrete
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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We examine quantum extensions of the continuous Painlevé equations, expressed as systems of first-order differential equations for non-commuting objects. We focus on the Painlevé equations II, IV and V. From their auto-Bäcklund transformations we derive the contiguity relations which we interpret as the quantum analogues of the discrete Painlevé equations.
Mots-clés : discrete systems; quantization; Painlevé equations. 
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     title = {Quantum {Painlev\'e} {Equations:} from {Continuous} to {Discrete}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a50/}
}
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Hajime Nagoya; Basil Grammaticos; Alfred Ramani. Quantum Painlevé Equations: from Continuous to Discrete. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a50/

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