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Continuous, Discrete and Ultradiscrete Painlevé Equations

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Symmetries and Integrability of Difference Equations

Part of the book series: CRM Series in Mathematical Physics ((CRM))

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Abstract

We give an introductory lecture on the theory of Painlevé equations, which are one of the most important objects in the theory of integrable systems, and their discrete counterparts. The lecture is divided into three parts: the Painlevé equations, discrete Painlevé equations and ultradiscrete Painlevé equations.

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Acknowledgements

Authors thank Profs. Tetsuji Tokihiro, Masatoshi Noumi and Akane Nakamura for helpful comments.

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Authors and Affiliations

  1. Department of Physics and Mathematics, Aoyama Gakuin University, Sagamihara, Kanagawa, 229-8558, Japan

    Nobutaka Nakazono

  2. School of Mathematics and Statistics, The University of Sydney, Carslaw Building F07, Sydney, NSW, 2006, Australia

    Yang Shi

  3. Faculty of Engineering Science, Kansai University, 3-3-35 Yamate, Suita, Osaka, 564-8680, Japan

    Masataka Kanki

Authors
  1. Nobutaka Nakazono
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  2. Yang Shi
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Correspondence to Masataka Kanki .

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Editors and Affiliations

  1. Mathematics and Physics Departments, and INFN, Sezione Roma Tre, Roma Tre University, Roma, Italy

    Decio Levi

  2. Collège Ahuntsic, Montréal, Québec, Canada

    Raphaël Rebelo

  3. Centre de Recherches Mathématiques and Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada

    Pavel Winternitz

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Nakazono, N., Shi, Y., Kanki, M. (2017). Continuous, Discrete and Ultradiscrete Painlevé Equations. In: Levi, D., Rebelo, R., Winternitz, P. (eds) Symmetries and Integrability of Difference Equations. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-56666-5_1

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