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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
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
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
Linking options:
https://www.mathnet.ru/eng/rcd621 https://www.mathnet.ru/eng/rcd/v12/i2/p198
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