Global Meromorphy of Solutions of the Painlevé Equations and Their Hierarchies

Proceedings of the Steklov Institute of Mathematics - Tập 311 - Trang 98-113 - 2021
A. V. Domrin1,2, B. I. Suleimanov2, M. A. Shumkin1
1Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
2Institute of Mathematics with Computing Centre, Subdivision of the Ufa Federal Research Centre of Russian Academy of Sciences, Ufa, Russia

Tóm tắt

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.

Tài liệu tham khảo

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