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Differentsial'nye Uravneniya, 1965, Volume 1, Number 1, Pages 79–81 (Mi de6713)  

This article is cited in 16 scientific papers (total in 16 papers)

On the rational solutions of the second Painlevé equation

A. P. Vorob'ev

Institute of Mathematics, Academy of Sciences Byelorussian SSR
Received: 30.10.1964
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. P. Vorob'ev, “On the rational solutions of the second Painlevé equation”, Differ. Uravn., 1:1 (1965), 79–81
Citation in format AMSBIB
\Bibitem{Vor65}
\by A.~P.~Vorob'ev
\paper On the rational solutions of the second Painlev\'e equation
\jour Differ. Uravn.
\yr 1965
\vol 1
\issue 1
\pages 79--81
\mathnet{http://mi.mathnet.ru/de6713}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=188519}
Linking options:
  • https://www.mathnet.ru/eng/de6713
  • https://www.mathnet.ru/eng/de/v1/i1/p79
  • This publication is cited in the following 16 articles:
    1. Peter A. Clarkson, Chun-Kong Law, Chia-Hua Lin, “A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation”, SIGMA, 19 (2023), 080, 20 pp.  mathnet  crossref
    2. I. A. Bobrova, “On symmetries of the nonstationary P(n)II hierarchy and their applications”, Theoret. and Math. Phys., 213:1 (2022), 1369–1394  mathnet  crossref  crossref  mathscinet  adsnasa
    3. Nikolay A. Kudryashov, “Lax Pairs and Rational Solutions of Similarity Reductions for Kupershmidt and Sawada – Kotera Hierarchies”, Regul. Chaotic Dyn., 26:3 (2021), 271–292  mathnet  crossref  mathscinet
    4. Nikolay A. Kudryashov, “Lax Pairs and Special Polynomials Associated with Self-similar Reductions of Sawada – Kotera and Kupershmidt Equations”, Regul. Chaotic Dyn., 25:1 (2020), 59–77  mathnet  crossref
    5. Nikolay A. Kudryashov, “Rational Solutions of Equations Associated with the Second Painlevé Equation”, Regul. Chaotic Dyn., 25:3 (2020), 273–280  mathnet  crossref
    6. Peter A. Clarkson, “Open Problems for Painlevé Equations”, SIGMA, 15 (2019), 006, 20 pp.  mathnet  crossref
    7. Nikolay A. Kudryashov, “Rational and Special Solutions for Some Painlevé Hierarchies”, Regul. Chaotic Dyn., 24:1 (2019), 90–100  mathnet  crossref
    8. Colin Rogers, Peter A. Clarkson, “Ermakov–Painlevé II Symmetry Reduction of a Korteweg Capillarity System”, SIGMA, 13 (2017), 018, 20 pp.  mathnet  crossref
    9. Peter D. Miller, Yue Sheng, “Rational Solutions of the Painlevé-II Equation Revisited”, SIGMA, 13 (2017), 065, 29 pp.  mathnet  crossref
    10. Nikolay A. Kudryashov, “Higher Painlevé Transcendents as Special Solutions of Some Nonlinear Integrable Hierarchies”, Regul. Chaotic Dyn., 19:1 (2014), 48–63  mathnet  crossref  mathscinet  zmath
    11. Pieter Roffelsen, “On the Number of Real Roots of the Yablonskii–Vorob'ev Polynomials”, SIGMA, 8 (2012), 099, 9 pp.  mathnet  crossref  mathscinet
    12. Kazuhide Matsuda, “Rational Solutions of the Sasano System of Type A(2)5”, SIGMA, 7 (2011), 030, 20 pp.  mathnet  crossref  mathscinet
    13. Pieter Roffelsen, “Irrationality of the Roots of the Yablonskii–Vorob'ev Polynomials and Relations between Them”, SIGMA, 6 (2010), 095, 11 pp.  mathnet  crossref  mathscinet
    14. M. V. Demina, N. A. Kudryashov, “Special polynomials and rational solutions of the hierarchy of the second Painlevé equation”, Theoret. and Math. Phys., 153:1 (2007), 1398–1406  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. A. V. Kitaev, “Elliptic asymptotics of the first and the second Painlevé transcendents”, Russian Math. Surveys, 49:1 (1994), 81–150  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. A. A. Kapaev, “Asymptotic expressions for the second Painlevй functions”, Theoret. and Math. Phys., 77:3 (1988), 1227–1234  mathnet  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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