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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2025 Volume 216, Number 8, Pages 129–154 (Mi sm10139)

Meromorphy of solutions for a system of $N$ equations of Painlevé 34 type related to negative symmetries of the Korteweg–de Vries equation

A. V. Domrinab, B. I. Suleimanovb

a Lomonosov Moscow State University, Moscow, Russia
b Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russia

Abstract: We prove the property of meromorphic extendability for every local holomorphic solution of a system of nonlinear nonautonomous ordinary differential equations. This system is a vector generalization of Painlevé's 34 equation (which is in its turn equivalent to the second Painlevé equation) and coincides with the stationary part of the symmetry of the Korteweg–de Vries equation obtained as the sum of the stationary parts of the classical Galilean symmetry and $N$ negative symmetries of this integrable evolutionary equation.
Bibliography: 39 titles.

Keywords: Painlevé equation, Painlevé property, Painlevé test, meromorphic extendability, Laurent series.

MSC: 34M05, 34M55

Received: 14.06.2024 and 24.04.2025

DOI: 10.4213/sm10139


 English version:
Sbornik: Mathematics, 2025, 216:8, 1138–1161


© Steklov Math. Inst. of RAS, 2025