Olga Efimova
Kashirskoe sh. 31, Moscow 115409, Russia
Department of Applied Mathematics, Moscow Engineering and Physics Institute
Publications:
Efimova O. Y., Kudryashov N. A.
Power Expansions for the SelfSimilar Solutions of the Modified Sawada–Kotera Equation
2007, vol. 12, no. 2, pp. 198218
Abstract
The fourthorder ordinary differential equation that denes the selfsimilar solutions of the Kaup–Kupershmidt and Sawada–Kotera equations is studied. This equation belongs to the class of fourthorder analogues of the Painlevé equations. All the power and nonpower 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.
