The sigma form of the second Painlevé hierarchy

Irina Bobrova, Marta Mazzocco

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Abstract

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.
Original languageEnglish
Article number104271
Number of pages8
JournalJournal of Geometry and Physics
Volume166
Early online date7 May 2021
DOIs
Publication statusPublished - Aug 2021

Bibliographical 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.

Keywords

  • Painlevé equations
  • Sigma forms
  • Sigma – coordinates

ASJC Scopus subject areas

  • Mathematical Physics
  • General Physics and Astronomy
  • Geometry and Topology

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