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Regular and Chaotic Dynamics, 2007, Volume 12, Issue 2, Pages 198–218
DOI: https://doi.org/10.1134/S1560354707020062 (Mi rcd621) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Power Expansions for the Self-Similar Solutions of the Modified Sawada–Kotera Equation

O. Yu. Efimova, N. A. Kudryashov

Department of Applied Mathematics, Moscow Engineering and Physics Institute, Kashirskoe sh. 31, Moscow 115409, Russia
Citations (1)
DOI: https://doi.org/10.1134/S1560354707020062
Abstract: The fourth-order ordinary differential equation that denes the self-similar solutions of the Kaup–Kupershmidt and Sawada–Kotera equations is studied. This equation belongs to the class of fourth-order analogues of the Painlevé equations. All the power and non-power asymptotic forms and expansions near points $z = 0, z = \infty$ and near an arbitrary point $z = z_0$ are found by means of power geometry methods. The exponential additions to the solutions of the studied equation are also determined.
Keywords: Kaup–Kupershmidt equation, Sawada–Kotera equation, fourth-order analogue of the second Painlevé equation, power geometry methods, asymptotic forms, power expansions.
Received: 15.06.2006
Accepted: 15.01.2007
Bibliographic databases:
Document Type: Article
MSC: 34E05, 58K55, 34A26, 34A45
Language: English
Citation: O. Yu. Efimova, N. A. Kudryashov, “Power Expansions for the Self-Similar Solutions of the Modified Sawada–Kotera Equation”, Regul. Chaotic Dyn., 12:2 (2007), 198–218
Citation in format AMSBIB
\Bibitem{EfiKud07}
\by O. Yu. Efimova, N. A. Kudryashov
\paper Power Expansions for the Self-Similar Solutions of the Modified Sawada–Kotera Equation
\jour Regul. Chaotic Dyn.
\yr 2007
\vol 12
\issue 2
\pages 198--218
\mathnet{http://mi.mathnet.ru/rcd621}
\crossref{https://doi.org/10.1134/S1560354707020062}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2350306}
\zmath{https://zbmath.org/?q=an:1229.34085}
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