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Mat. Sb. (N.S.), 1987, Volume 134(176), Number 3(11), Pages 421–444 (Mi msb2768)  

This article is cited in 11 scientific papers (total in 11 papers)

The method of isomonodromy deformations and the asymptotics of solutions of the “complete” third Painlevé equation

A. V. Kitaev

Abstract:$2\times2$ matrix linear ordinary differential equation of the first order is considered whose coefficients depend on an additional parameter $\tau$ having two irregular first order singular points $\lambda=0$ and $\lambda=\infty$. The monodromy data of this equation as $\tau\to0$ and $\tau\to\infty$ are computed. These computations are used to find the asymptotics of the “degenerate” fifth Painlevé equation, which is equivalent to the “complete” third one. This is possible due to the connection of these Painlevé equations with isomonodromy deformations of the coefficients of the matrix linear equation. Bäcklund transformations and their application to asymptotic problems are considered in detail.
Bibliography: 42 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 62:2, 421–444

Bibliographic databases:

UDC: 517.9
MSC: Primary 34E05; Secondary 34A20, 34E20, 30D05
Received: 17.07.1986

Citation: A. V. Kitaev, “The method of isomonodromy deformations and the asymptotics of solutions of the “complete” third Painlevé equation”, Mat. Sb. (N.S.), 134(176):3(11) (1987), 421–444; Math. USSR-Sb., 62:2 (1989), 421–444

Citation in format AMSBIB
\by A.~V.~Kitaev
\paper The method of isomonodromy deformations and the asymptotics of solutions of the ``complete'' third Painlev\'e equation
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 134(176)
\issue 3(11)
\pages 421--444
\jour Math. USSR-Sb.
\yr 1989
\vol 62
\issue 2
\pages 421--444

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    This publication is cited in the following articles:
    1. A V Kitaev, J Phys A Math Gen, 23:15 (1990), 3543  crossref  mathscinet  zmath  adsnasa
    2. D. Levi, P. Winternitz, “Exact solutions of the stimulated-Raman-scattering equations”, Phys Rev A, 44:9 (1991), 6057  crossref  mathscinet  adsnasa  isi
    3. A V Kitaev, A V Rybin, J Timonen, J Phys A Math Gen, 26:14 (1993), 3583  crossref  mathscinet  zmath  adsnasa
    4. A. L. Kholodenko, A. L. Beyerlein, “Painlevé III and Manning's Counterion Condensation”, Phys Rev Letters, 74:23 (1995), 4679  crossref  adsnasa
    5. Youmin Lu, Bryce Mcleod, “Asymptotics of the nonnegative solutions of the general fifth Painlevé equation”, Applicable Analysis, 72:3-4 (1999), 501  crossref
    6. Costin O., “Correlation Between Pole Location and Asymptotic Behavior for Painlevé I Solutions”, Commun. Pure Appl. Math., 52:4 (1999), 461–478  crossref  mathscinet  zmath  isi
    7. Youmin Lu, Zhoude Shao, “Application of uniform asymptotica method to the asymptotics of the solutions of the fifth paonlevé equation when δ=0”, Applicable Analysis, 79:3-4 (2001), 335  crossref
    8. V.Yu. Novokshenov, “Level spacing functions and connection formulas for Painlevé V transcendent”, Physica D: Nonlinear Phenomena, 152-153 (2001), 225  crossref
    9. A. V. Kitaev, “Quadratic transformations for the third and fifth Painlevé equations”, J. Math. Sci. (N. Y.), 136:1 (2006), 3586–3595  mathnet  crossref  mathscinet  zmath  elib  elib
    10. A V Kitaev, A H Vartanian, “Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation: I”, Inverse Problems, 20:4 (2004), 1165  crossref  elib
    11. J. Math. Sci. (N. Y.), 192:1 (2013), 81–90  mathnet  crossref  mathscinet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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