Painlevé test for ordinary differential equations associated with the heat equation

A. V. Vinogradov

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider nonlinear ordinary differential equations up to the sixth order that are associated with the heat equation. Each of them is subjected to the Painlevé analysis. For the fourth- and sixth-order equations we obtain a criterion for having the Painlevé property; for the fifth-order equation we formulate necessary conditions for passing the Painlevé test. We also present a fifth-order equation analogous to the Chazy-$3$ equation.

UDC: 517.957

Received in November 2013

DOI: 10.1134/S0371968514030054

 English version: Proceedings of the Steklov Institute of Mathematics, 2014, 286, 65–76

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