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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 398, Pages 145–161 (Mi znsl5200)  
This article is cited in 1 scientific paper (total in 1 paper)

Parametric Painlevé equations

A. V. Kitaev

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
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Abstract: The parametric Painlevé equations are those ODEs whose general solutions can be presented in the parametric form in terms of the Painlevé functions. Most of these ODEs do not possess the Painlevé property. By considering similarity solutions of the short pulse equation and its decoupled generalization we derive a non-trivial example of the parametric Painlevé equation related with the third Painlevé equation. We also discuss some analytic properties of this equation describing the structure of movable singularities.
Key words and phrases: the Painlevé equations, isomonodromy deformations, Lax pair, short pulse equation.
Received: 19.03.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 192, Issue 1, Pages 81–90
DOI: https://doi.org/10.1007/s10958-013-1375-9
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Citation: A. V. Kitaev, “Parametric Painlevé equations”, Questions of quantum field theory and statistical physics. Part 22, Zap. Nauchn. Sem. POMI, 398, POMI, St. Petersburg, 2012, 145–161; J. Math. Sci. (N. Y.), 192:1 (2013), 81–90
Citation in format AMSBIB
\Bibitem{Kit12}
\by A.~V.~Kitaev
\paper Parametric Painlev\'e equations
\inbook Questions of quantum field theory and statistical physics. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 398
\pages 145--161
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5200}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2944993}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 192
\issue 1
\pages 81--90
\crossref{https://doi.org/10.1007/s10958-013-1375-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884979853}
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  • https://www.mathnet.ru/eng/znsl/v398/p145
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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