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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 122, Number 1, Pages 5–22
DOI: https://doi.org/10.4213/tmf551
(Mi tmf551)
 

This article is cited in 13 scientific papers (total in 13 papers)

On the relation between the continuous and discrete Painlevé equations

P. A. Clarkson, E. L. Mansfield, H. N. Webster

University of Kent
References:
Abstract: A method for deriving difference equations (the discrete Painlevé equations in particular) from the Bäcklund transformations of the continuous Painlevé equations is discussed. This technique can be used to derive several of the known discrete Painlevé equations (in particular, the first and second discrete Painlevé equations and some of their alternative versions). The Painlevé equations possess hierarchies of rational solutions and one-parameter families of solutions expressible in terms of the classical special functions for special values of the parameters. Hence, the aforementioned relations can be used to generate hierarchies of exact solutions for the associated discrete Painlevé equations. Exact solutions of the Painlevé equations simultaneously satisfy both a differential equation and a difference equation, analogously to the special functions.
English version:
Theoretical and Mathematical Physics, 2000, Volume 122, Issue 1, Pages 1–16
DOI: https://doi.org/10.1007/BF02551165
Bibliographic databases:
Language: Russian
Citation: P. A. Clarkson, E. L. Mansfield, H. N. Webster, “On the relation between the continuous and discrete Painlevé equations”, TMF, 122:1 (2000), 5–22; Theoret. and Math. Phys., 122:1 (2000), 1–16
Citation in format AMSBIB
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\by P.~A.~Clarkson, E.~L.~Mansfield, H.~N.~Webster
\paper On the relation between the continuous and discrete Painlev\'e equations
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\yr 2000
\vol 122
\issue 1
\pages 5--22
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\crossref{https://doi.org/10.4213/tmf551}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1776503}
\zmath{https://zbmath.org/?q=an:0994.34077}
\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 122
\issue 1
\pages 1--16
\crossref{https://doi.org/10.1007/BF02551165}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000086224200002}
Linking options:
  • https://www.mathnet.ru/eng/tmf551
  • https://doi.org/10.4213/tmf551
  • https://www.mathnet.ru/eng/tmf/v122/i1/p5
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:463
    Full-text PDF :212
    References:53
    First page:1
     
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