The sigma form of the second Painlevé hierarchy

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  • National Research University Higher School of Economics


In this paper we study the so-called sigma form of the second Painlevé hierarchy. To obtain this form, we use some properties of the Hamiltonian structure of the second Painlevé hierarchy and of the Lenard operator.

Bibliographic note

Funding Information: Acknowledgments. The authors would like to express their gratitude to Volodya Rubtsov for introducing them to each other. The authors are also grateful to Vladimir Poberezhnyi, who initiated I.B. to the Painlev? equations theory and constantly supported her during her scientific work. The research of I.B. is a part of her PhD program studies at the Higher School of Economics (HSE University). I.B. would like to thank to Faculty of Mathematics for giving her such opportunity. The research of M.M. is supported by the EPSRC Research Grant EP/P021913/1. The research of I.B. was partially supported by the RFBR Grant 18-01-00461 A.


Original languageEnglish
Article number104271
Number of pages8
JournalJournal of Geometry and Physics
Early online date7 May 2021
Publication statusE-pub ahead of print - 7 May 2021


  • Painlevé equations, Sigma forms, Sigma – coordinates