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Symmetry, Integrability and Geometry: Methods and Applications Quantum Painlevé Equations: from Continuous to Discrete

By Hajime Nagoya, Basil Grammaticos and Alfred Ramani

Abstract

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. Key words: discrete systems; quantization; Painlevé equations 2000 Mathematics Subject Classification: 34M55; 37K55; 81S99

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.193.3418
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