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Regular and Chaotic Dynamics, 2020, Volume 25, Issue 3, Pages 273–280
DOI: https://doi.org/10.1134/S156035472003003X (Mi rcd1063) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Rational Solutions of Equations Associated with the Second Painlevé Equation

Nikolay A. Kudryashov

Department of Applied Mathematics, National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia
Citations (4)
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DOI: https://doi.org/10.1134/S156035472003003X
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.
Keywords: second Painlevé equation, Painlevé test, Yablonskii – Vorob'ev polynomials, rational solution.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10025
This reported study was funded by the Russian Foundation for Basic Research (RFBR) according to the research project No. 18-29-10025.
Received: 04.02.2020
Accepted: 11.03.2020
Bibliographic databases:
Document Type: Article
MSC: 34M55
Language: English
Citation: Nikolay A. Kudryashov, “Rational Solutions of Equations Associated with the Second Painlevé Equation”, Regul. Chaotic Dyn., 25:3 (2020), 273–280
Citation in format AMSBIB
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\by Nikolay A. Kudryashov
\paper Rational Solutions of Equations Associated with the Second Painlevé Equation
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 3
\pages 273--280
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\crossref{https://doi.org/10.1134/S156035472003003X}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85085544274}
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    • This publication is cited in the following 4 articles:
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    Abstract page:115
    References:28
     
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