Abstract:
It is shown that self-similar solutions of the Einstein-Maxwell equations in the axially symmetric case describe isomonodromic deformations of ordinary differential equations with rational coefficients. New types of these solutions that expressed in terms of fifth Painleve trancedent are found.
Citation:
A. V. Kitaev, “The isomonodromic deformations and similarity solutions of the Einstein–Maxwell equations”, Differential geometry, Lie groups and mechanics. Part 11, Zap. Nauchn. Sem. LOMI, 181, "Nauka", Leningrad. Otdel., Leningrad, 1990, 65–92; J. Soviet Math., 62:2 (1992), 2646–2663
\Bibitem{Kit90}
\by A.~V.~Kitaev
\paper The isomonodromic deformations and similarity solutions of the Einstein--Maxwell equations
\inbook Differential geometry, Lie groups and mechanics. Part~11
\serial Zap. Nauchn. Sem. LOMI
\yr 1990
\vol 181
\pages 65--92
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4728}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1097580}
\zmath{https://zbmath.org/?q=an:0784.35116|0727.35133}
\transl
\jour J. Soviet Math.
\yr 1992
\vol 62
\issue 2
\pages 2646--2663
\crossref{https://doi.org/10.1007/BF01102636}
Linking options:
https://www.mathnet.ru/eng/znsl4728
https://www.mathnet.ru/eng/znsl/v181/p65
This publication is cited in the following 1 articles:
H. M. Babujian, A. V. Kitaev, “Generalized Knizhnik–Zamolodchikov equations and isomonodromy quantization of the equations integrable via the Inverse Scattering Transform: Maxwell–Bloch system with pumping”, Journal of Mathematical Physics, 39:5 (1998), 2499
Citation in format AMSBIB
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