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arXiv · 0806.1466

Quantum Painlevé Equations: from Continuous to Discrete

Hajime Nagoya·Basil Grammaticos·Alfred Ramani
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Abstract

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.

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Hajime Nagoya, Basil Grammaticos, Alfred Ramani. 2008-06-09. Quantum Painlevé Equations: from Continuous to Discrete. https://doi.org/10.3842/sigma.2008.051

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