D. S. Noshchenko, I. A. Ilyin, “Symmetry groups for Painleve equations”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2012, Number 2(5),Pages <nobr>7

MATHEMATICS

Symmetry groups for Painleve equations

D. S. Noshchenko^a, I. A. Ilyin^ba

^a Vitus Bering Kamchatka State University, 683032, Petropavlovsk-Kamchatsky, Pogranichnaya st., 4, Russia
^b Institute of Cosmophysical Researches and Radio Wave Propagation Far-Eastern Branch, Russian Academy of Sciences, 684034, Kamchatskiy Kray, Paratunka, Mirnaya st., 7

Abstract: In this study, one-parametric symmetry groups were found for 50 canonical equations with Painleve property, and, in special cases, general solutions were obtained. The result can be used as reference for specialists in the theory of nonlinear differential equations.

Keywords: differential equation, singularities, Painleve property, symmetry groups.

UDC: 517.956

MSC: 70G65

Received: 16.10.2012

DOI: 10.18454/2079-6641-2012-5-2-7-17