Continuous, Discrete and Ultradiscrete Painlevé Equations

  • Nobutaka Nakazono
  • Yang Shi
  • Masataka Kanki
Part of the CRM Series in Mathematical Physics book series (CRM)


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.



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


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Physics and MathematicsAoyama Gakuin UniversitySagamihara, KanagawaJapan
  2. 2.School of Mathematics and StatisticsThe University of SydneySydneyAustralia
  3. 3.Faculty of Engineering ScienceKansai UniversityOsakaJapan

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