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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 286, Pages 75–87
DOI: https://doi.org/10.1134/S0371968514030054 (Mi tm3572) 		 
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
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DOI: https://doi.org/10.1134/S0371968514030054
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.
Received in November 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 286, Pages 65–76
DOI: https://doi.org/10.1134/S0081543814060054
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: A. V. Vinogradov, “Painlevé test for ordinary differential equations associated with the heat equation”, Algebraic topology, convex polytopes, and related topics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 286, MAIK Nauka/Interperiodica, Moscow, 2014, 75–87; Proc. Steklov Inst. Math., 286 (2014), 65–76
Citation in format AMSBIB
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\by A.~V.~Vinogradov
\paper Painlev\'e test for ordinary differential equations associated with the heat equation
\inbook Algebraic topology, convex polytopes, and related topics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 286
\pages 75--87
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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