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.
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
\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://mathscinet.ams.org/mathscinet-getitem?mr=2120830}
\zmath{https://zbmath.org/?q=an:1083.34065}
\elib{https://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{https://elibrary.ru/item.asp?id=13519008}
Linking options:
https://www.mathnet.ru/eng/znsl717
https://www.mathnet.ru/eng/znsl/v317/p105
This publication is cited in the following 4 articles:
Arata Komyo, “A Nonclassical Algebraic Solution of a 3-Variable Irregular Garnier System”, FE, 67:1 (2024), 85
Karamoko Diarra, Frank Loray, “Classification of algebraic solutions of irregular Garnier systems”, Compositio Math., 156:5 (2020), 881
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.
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.
Citation in format AMSBIB
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