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 π/2 (modπ). These connection formulas lead to the determination of the asymptotics of the eigenvalues for the Sturm–Liouville equation with a cubic nonlinearity.
Citation:
M. V. Karasev, A. V. Pereskokov, “On connection formulas for the second Painleve transcendent. Proof of the Miles conjecture, and a quantization rule”, Russian Acad. Sci. Izv. Math., 42:3 (1994), 501–560
\Bibitem{KarPer93}
\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 Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 42
\issue 3
\pages 501--560
\mathnet{http://mi.mathnet.ru/eng/im870}
\crossref{https://doi.org/10.1070/IM1994v042n03ABEH001544}
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\zmath{https://zbmath.org/?q=an:0815.34046}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..42..501K}
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Linking options:
https://www.mathnet.ru/eng/im870
https://doi.org/10.1070/IM1994v042n03ABEH001544
https://www.mathnet.ru/eng/im/v57/i3/p92
This publication is cited in the following 4 articles:
S. A. Stepin, A. I. Shafarevich, “WKB method for nonlinear equations of Emden–Fowler type”, Dokl. Math., 105:1 (2022), 39–44
Yoshitsugu Takei, “On an exact WKB approach to Ablowitz-Segur's connection problem for the second Painlevé equation”, Anziam J, 44:1 (2002), 111
M. V. Karasev, A. V. Pereskokov, “Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. I. The model with logarithmic singularity”, Izv. Math., 65:5 (2001), 883–921
Citation in format AMSBIB
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