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Zap. Nauchn. Sem. POMI, 2004, Volume 317, Pages 105–121 (Mi znsl717)  

This article is cited in 2 scientific papers (total in 2 papers)

Quadratic transformations for the third and fifth Painlevé equations

A. V. Kitaev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: Quadratic transformations for the third and fifth Painlevé equations are constructed via the method of $RS$-transformations. This method can be viewed as a prolongation of the quadratic transformations for the Painlevé equations to the associated linear ODEs, whose isomonodromy deformations are governed by the corresponding Painlevé equations.

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English version:
Journal of Mathematical Sciences (New York), 2006, 136:1, 3586–3595

Bibliographic databases:

UDC: 517.9
Received: 26.06.2004

Citation: A. V. Kitaev, “Quadratic transformations for the third and fifth Painlevé equations”, Questions of quantum field theory and statistical physics. Part 18, Zap. Nauchn. Sem. POMI, 317, POMI, St. Petersburg, 2004, 105–121; J. Math. Sci. (N. Y.), 136:1 (2006), 3586–3595

Citation in format AMSBIB
\Bibitem{Kit04}
\by A.~V.~Kitaev
\paper Quadratic transformations for the third and fifth Painlev\'e equations
\inbook Questions of quantum field theory and statistical physics. Part~18
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 317
\pages 105--121
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl717}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2120830}
\zmath{https://zbmath.org/?q=an:1083.34065}
\elib{http://elibrary.ru/item.asp?id=9129823}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 136
\issue 1
\pages 3586--3595
\crossref{https://doi.org/10.1007/s10958-006-0184-9}
\elib{http://elibrary.ru/item.asp?id=13519008}


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    This publication is cited in the following articles:
    1. Joshi N., Kitaev A.V., Treharne P.A., “On the linearization of the Painlevé III–VI equations and reductions of the three-wave resonant system”, J. Math. Phys., 48:10 (2007), 103512, 42 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    2. Joshi N., Kitaev A.V., Treharne P.A., “On the linearization of the first and second Painlevé equations”, J. Phys. A, 42:5 (2009), 055208, 18 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Записки научных семинаров ПОМИ
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