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TMF, 2003, Volume 134, Number 1, Pages 101–109 (Mi tmf143)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Fourth Painlevé Hierarchy

N. A. Kudryashov

Moscow Engineering Physics Institute (State University)

Abstract: We use the inverse monodromy transform to find the fourth Painlevé hierarchy. The second and third members of this hierarchy are given. Special and rational solutions of the second and third members for the $P_4$ hierarchy are discussed. We apply the Painlevé test to the second member of the fourth Painlevé hierarchy.

Keywords: fourth Painlevé hierarchy, fourth Painlevé equation, Painlevé test, special and rational solutions

DOI: https://doi.org/10.4213/tmf143

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English version:
Theoretical and Mathematical Physics, 2003, 134:1, 86–93

Bibliographic databases:


Citation: N. A. Kudryashov, “On the Fourth Painlevé Hierarchy”, TMF, 134:1 (2003), 101–109; Theoret. and Math. Phys., 134:1 (2003), 86–93

Citation in format AMSBIB
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\by N.~A.~Kudryashov
\paper On the Fourth Painlev\'e Hierarchy
\jour TMF
\yr 2003
\vol 134
\issue 1
\pages 101--109
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2021733}
\zmath{https://zbmath.org/?q=an:1109.34344}
\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 134
\issue 1
\pages 86--93
\crossref{https://doi.org/10.1023/A:1021871723852}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000181042100008}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Filipuk, GV, “The symmetric fourth Painlevé hierarchy and associated special polynomials”, Studies in Applied Mathematics, 121:2 (2008), 157  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Conde J.M., Gordoa P.R., Pickering A., “Backlund Transformations for New Fourth Painlevé Hierarchies”, Commun. Nonlinear Sci. Numer. Simul., 19:3 (2014), 448–458  crossref  mathscinet  adsnasa  isi  scopus  scopus
    3. Gordoa P.R., Pickering A., Wattis J.A.D., “Nonisospectral Scattering Problems and Similarity Reductions”, Appl. Math. Comput., 237 (2014), 77–84  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Gordoa P.R., Pickering A., “Backlund Transformations For a New Extended Painleve Hierarchy”, Commun. Nonlinear Sci. Numer. Simul., 69 (2019), 78–97  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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