Olga Efimova

Kashirskoe sh. 31, Moscow 115409, Russia
Department of Applied Mathematics, Moscow Engineering and Physics Institute


Efimova O. Y., Kudryashov N. A.
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
Citation: Efimova O. Y., Kudryashov N. A.,  Power Expansions for the Self-Similar Solutions of the Modified Sawada–Kotera Equation, Regular and Chaotic Dynamics, 2007, vol. 12, no. 2, pp. 198-218

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