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Russian Academy of Sciences. Izvestiya Mathematics, 1994, Volume 42, Issue 3, Pages 501–560
DOI: https://doi.org/10.1070/IM1994v042n03ABEH001544 (Mi im870) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On connection formulas for the second Painleve transcendent. Proof of the Miles conjecture, and a quantization rule

M. V. Karasev, A. V. Pereskokov
English version PDF (2467 kB) Citations (4)
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DOI: https://doi.org/10.1070/IM1994v042n03ABEH001544
Abstract: The method of isomonodromy deformations is used to prove connection formulas for the second Painleve transcendent, which is exponentially decreasing on one side of a turning point and has a Kuzmak–Luke–Whitham decomposition on the other. The phase advance turns out to be equal to $\pi/2$ ($\operatorname{mod}\pi$). These connection formulas lead to the determination of the asymptotics of the eigenvalues for the Sturm–Liouville equation with a cubic nonlinearity.
Received: 27.12.1991
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1993, Volume 57, Issue 3, Pages 92–151
Bibliographic databases:
UDC: 517.946+517.958
MSC: Primary 34E20, 34E05; Secondary 34B24, 34A34, 34C15, 81S99
Language: English
Original paper language: Russian
Citation: M. V. Karasev, A. V. Pereskokov, “On connection formulas for the second Painleve transcendent. Proof of the Miles conjecture, and a quantization rule”, Izv. RAN. Ser. Mat., 57:3 (1993), 92–151; Russian Acad. Sci. Izv. Math., 42:3 (1994), 501–560
Citation in format AMSBIB
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\by M.~V.~Karasev, A.~V.~Pereskokov
\paper On connection formulas for the second Painleve transcendent. Proof of the Miles conjecture, and a quantization rule
\jour Izv. RAN. Ser. Mat.
\yr 1993
\vol 57
\issue 3
\pages 92--151
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\zmath{https://zbmath.org/?q=an:0815.34046}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..42..501K}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 42
\issue 3
\pages 501--560
\crossref{https://doi.org/10.1070/IM1994v042n03ABEH001544}
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  • https://www.mathnet.ru/eng/im/v57/i3/p92
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:448
    Russian version PDF:145
    English version PDF:13
    References:69
    First page:2
     
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