Email this article Distribution of poles of real-valued solutions of the third Painleve equation $P_{\mathrm{III}}^{(6)}$
- Authors: Novokshenov V.Y.1
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Affiliations:
- Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russia
- Issue: Vol 216, No 8 (2025)
- Pages: 155-170
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/306731
- DOI: https://doi.org/10.4213/sm10068
- ID: 306731
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Abstract
We study a two-parameter family of real solutions of a special Painleve equation of the third kind,which is used in many models of mathematical physics. Using the method of isomonodromic deformations we construct asymptotic formulae as $x\to\infty$ on the real semi-axis, including the distribution of poles of the singular solution. For $n\gg1$ we show that there are no real poles with $x
About the authors
Victor Yur'evich Novokshenov
Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russia
Author for correspondence.
Email: novik53@mail.ru
Doctor of physico-mathematical sciences, Professor
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