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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
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.
Received: 04.02.2020 Accepted: 11.03.2020
Citation:
Nikolay A. Kudryashov, “Rational Solutions of Equations Associated with the Second Painlevé Equation”, Regul. Chaotic Dyn., 25:3 (2020), 273–280
Linking options:
https://www.mathnet.ru/eng/rcd1063 https://www.mathnet.ru/eng/rcd/v25/i3/p273
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Abstract page: | 116 | References: | 28 |
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