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Teoreticheskaya i Matematicheskaya Fizika, 1988, Volume 77, Number 3, Pages 323–332 (Mi tmf6023)  
This article is cited in 22 scientific papers (total in 22 papers)

Asymptotic expressions for the second Painlevé functions

A. A. Kapaev
Full-text PDF (1021 kB) Citations (22)
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Abstract: The method of isomonodromicJdeformations is used to investigate the asymptotic properties of solutions of the second Painlevé equation (I). The leading terms as $x\to\pm\infty$ of the second Painlevé functions are constructed for the general case. The parameters of the asymptotic behavior are expressed in terms of first inteErals of the Painlevé equation, which are the monodromy data of the associated system (2) of linear ordinary differential equations with rational coefficients. The asymptotic behaviors of the real and imaginary second Painlevé functions are separated.
Received: 02.06.1987
English version:
Theoretical and Mathematical Physics, 1988, Volume 77, Issue 3, Pages 1227–1234
DOI: https://doi.org/10.1007/BF01016976
Bibliographic databases:
Language: Russian
Citation: A. A. Kapaev, “Asymptotic expressions for the second Painlevé functions”, TMF, 77:3 (1988), 323–332; Theoret. and Math. Phys., 77:3 (1988), 1227–1234
Citation in format AMSBIB
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\by A.~A.~Kapaev
\paper Asymptotic expressions for the second Painlevé functions
\jour TMF
\yr 1988
\vol 77
\issue 3
\pages 323--332
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=982412}
\zmath{https://zbmath.org/?q=an:0692.34061}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 77
\issue 3
\pages 1227--1234
\crossref{https://doi.org/10.1007/BF01016976}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988AK72200001}
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    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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