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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 134, Number 1, Pages 101–109
DOI: https://doi.org/10.4213/tmf143 (Mi tmf143) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the Fourth Painlevé Hierarchy

N. A. Kudryashov

Moscow Engineering Physics Institute (State University)
Full-text PDF (168 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf143
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 P4 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.
English version:
Theoretical and Mathematical Physics, 2003, Volume 134, Issue 1, Pages 86–93
DOI: https://doi.org/10.1023/A:1021871723852
Bibliographic databases:
Language: Russian
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
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\pages 101--109
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\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 134
\issue 1
\pages 86--93
\crossref{https://doi.org/10.1023/A:1021871723852}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000181042100008}
Linking options:
  • https://www.mathnet.ru/eng/tmf143
  • https://doi.org/10.4213/tmf143
  • https://www.mathnet.ru/eng/tmf/v134/i1/p101
    • This publication is cited in the following 6 articles:
    1. V. I. Anoshin, A. D. Beketova, A. V. Parusnikova, E. D. Prokopenko, “Convergence of formal solutions to the second member of the fourth Painlevé hierarchy in a neighborhood of zero”, Comput. Math. Math. Phys., 63:1 (2023), 86–95  mathnet  mathnet  crossref  crossref
    2. Anoshin I V., Beketova A.D., Parusnikova V A., Romanov V K., “Asymptotic Expansions of Solutions to the Second Term of the Fourth Painleve Hierarchy”, Program. Comput. Softw., 48:1 (2022), 30–35  crossref  mathscinet  isi
    3. 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
    4. 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
    5. 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
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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