Rational Solutions of Equations Associated with the Second Painlevé Equation

Abstract

Nonlinear differential equations associated with the second Painlevé equation are considered. Transformations for solutions of the singular manifold equation are presented. It is shown that rational solutions of the singular manifold equation are determined by means of the Yablonskii-Vorob’ev polynomials. It is demonstrated that rational solutions for some differential equations are also expressed via the Yablonskii-Vorob’ev polynomials.

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Funding

This reported study was funded by the Russian Foundation for Basic Research (RFBR) according to the research project No. 18-29-10025.

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Correspondence to Nikolay A. Kudryashov.

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The authors declare that they have no conflicts of interest.

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Kudryashov, N.A. Rational Solutions of Equations Associated with the Second Painlevé Equation. Regul. Chaot. Dyn. 25, 273–280 (2020). https://doi.org/10.1134/S156035472003003X

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Keywords

  • second Painlevé equation
  • Painlevé test
  • Yablonskii-Vorob’ev polynomials
  • rational solution

MSC2010 numbers

  • 34M55