Quantum Painlev\'e Equations: from Continuous to Discrete
Quantum Algebra
2010-12-17 v1 Classical Analysis and ODEs
Exactly Solvable and Integrable Systems
Abstract
We examine quantum extensions of the continuous Painlev\'e equations, expressed as systems of first-order differential equations for non-commuting objects. We focus on the Painlev\'e equations II, IV and V. From their auto-B\"acklund transformations we derive the contiguity relations which we interpret as the quantum analogues of the discrete Painlev\'e equations.
Cite
@article{arxiv.0806.1466,
title = {Quantum Painlev\'e Equations: from Continuous to Discrete},
author = {Hajime Nagoya and Basil Grammaticos and Alfred Ramani},
journal= {arXiv preprint arXiv:0806.1466},
year = {2010}
}
Comments
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/