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Trudy Mat. Inst. Steklova, 2020, Volume 311, Pages 106–122 (Mi tm4116)  

Global Meromorphy of Solutions of the Painlevé Equations and Their Hierarchies

A. V. Domrinab, B. I. Suleimanovb, M. A. Shumkina

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia
b Institute of Mathematics with Computing Centre, Subdivision of the Ufa Federal Research Centre of Russian Academy of Sciences, ul. Chernyshevskogo 112, Ufa, 450008 Russia

Abstract: We show that all local holomorphic solutions of all equations constituting the hierarchies of the first and second Painlevé equations can be analytically continued to meromorphic functions on the whole complex plane. We also present a new conceptual proof of the fact that all local holomorphic solutions of the first, second, and fourth Painlevé equations are globally meromorphic.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00474
The work of the first author was supported by the Russian Foundation for Basic Research, project no. 19-01-00474.


DOI: https://doi.org/10.4213/tm4116

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 311, 98–113

Bibliographic databases:

UDC: 517.554+517.957
Received: March 7, 2020
Revised: March 31, 2020
Accepted: July 27, 2020

Citation: A. V. Domrin, B. I. Suleimanov, M. A. Shumkin, “Global Meromorphy of Solutions of the Painlevé Equations and Their Hierarchies”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 106–122; Proc. Steklov Inst. Math., 311 (2020), 98–113

Citation in format AMSBIB
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\paper Global Meromorphy of Solutions of the Painlev\'e Equations and Their Hierarchies
\inbook Analysis and mathematical physics
\bookinfo Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 311
\pages 106--122
\publ Steklov Math. Inst.
\publaddr Moscow
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