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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 2, Pages 179–190
(Mi timm818)
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This article is cited in 1 scientific paper (total in 1 paper)
Special solutions of the first and second Painlevé equations and singularities of the monodromy data manifold
V. Yu. Novokshenov Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Abstract:
A classification of solutions of the first and second Painlevé equations corresponding to a special distribution of poles at infinity is considered. The relation between this distribution and singularities of the two-dimensional complex monodromy data manifold used for the parameterization of the solutions is analyzed. It turns out that solutions of the Painlevé equations have no poles in a certain critical sector of the complex plane if and only if their monodromy data lie in the singularity submanifold. Such solutions belong to the so-called class of “truncated” solutions (intégrales tronquée) according to P. Boutroux's classification. It is shown that all known special solutions of the first and second Painlevé equations belong to this class.
Keywords:
Painlevé equations, isomonodromic deformations, distribution of poles, special solutions, Padé approximations.
Received: 20.09.2011
Citation:
V. Yu. Novokshenov, “Special solutions of the first and second Painlevé equations and singularities of the monodromy data manifold”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 179–190; Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 105–117
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https://www.mathnet.ru/eng/timm818 https://www.mathnet.ru/eng/timm/v18/i2/p179
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Abstract page: | 297 | Full-text PDF : | 145 | References: | 51 | First page: | 4 |
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