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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 051, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.051 (Mi sigma304) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Quantum Painlevé Equations: from Continuous to Discrete

Hajime Nagoyaa, Basil Grammaticosb, Alfred Ramanic

a Graduate School of Mathematical Sciences, The University of Tokyo, Japan
b IMNC, Université Paris VII \& XI, CNRS, UMR 8165, Bât. 104, 91406 Orsay, France
c Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France
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DOI: https://doi.org/10.3842/SIGMA.2008.051
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.
Keywords: discrete systems; quantization; Painlevé equations.
Received: March 5, 2008; in final form May 3, 2008; Published online June 9, 2008
Bibliographic databases:
Document Type: Article
MSC: 34M55; 37K55; 81S99
Language: English
Citation: Hajime Nagoya, Basil Grammaticos, Alfred Ramani, “Quantum Painlevé Equations: from Continuous to Discrete”, SIGMA, 4 (2008), 051, 9 pp.
Citation in format AMSBIB
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\by Hajime Nagoya, Basil Grammaticos, Alfred Ramani
\paper Quantum Painlev\'e Equations: from Continuous to Discrete
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\yr 2008
\vol 4
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    • This publication is cited in the following 6 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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