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

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

2006-06-15

arxiv.org/abs/nlin/0606042v3

Nonlinear Sciences

Exactly Solvable and Integrable Systems

31 pages, 9 figures

Scientific paper

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 Painlev\'{e} equations. All the power and non-power asymptotic forms and expansions near points $z=0$, $z=\infty$ and near arbitrary point $z=z_0$ are found by means of power geometry methods. The exponential additions to the solutions of studied equation are also determined.

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