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Power expansions for the self-similar solutions of the modified Savada-Kotera equation

Olga Yu. Efimova, Nikolai A. Kudryashov

nlin.SIarXiv:nlin/0606042

Abstract

The fourth-order ordinary differential equation, defining new transcendents, is studied. The self-similar solutions of the Kaup-Kupershmidt and Savada-Kotera equations are shown to be found taking its solutions into account. Equation studied 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=∞ and near arbitrary point z=z0 are found by means of power geometry methods. The exponential additions to the solutions of studied equation are also determined.

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