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Painlevé test for ordinary differential equations associated with the heat equation

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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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. V. Vinogradov

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  1. A. V. Vinogradov
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Correspondence to A. V. Vinogradov.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 286, pp. 75–87.

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Vinogradov, A.V. Painlevé test for ordinary differential equations associated with the heat equation. Proc. Steklov Inst. Math. 286, 65–76 (2014). https://doi.org/10.1134/S0081543814060054

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  • DOI: https://doi.org/10.1134/S0081543814060054

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