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 Ufimsk. Mat. Zh., 2012, Volume 4, Issue 2, Pages 13–27 (Mi ufa145)

Separation of an equation in the system of two second-order ordinary differential equations

Yu. Yu. Bagderina

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: We consider projectable type systems of two second-order ordinary differential equations with cubic nonlinearity of the right-hand side in first derivatives. For such systems we obtain criteria of reducibility by local transformation to a system with a separating equation in one of the unknown functions. Applications of the criteria and construction of the corresponding transformation is illustrated by a number of examples.

Keywords: second-order equation, decoupling of equations, separation of an equation, submersive system.

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Bibliographic databases:
UDC: 517.925

Citation: Yu. Yu. Bagderina, “Separation of an equation in the system of two second-order ordinary differential equations”, Ufimsk. Mat. Zh., 4:2 (2012), 13–27

Citation in format AMSBIB
\Bibitem{Bag12} \by Yu.~Yu.~Bagderina \paper Separation of an equation in the system of two second-order ordinary differential equations \jour Ufimsk. Mat. Zh. \yr 2012 \vol 4 \issue 2 \pages 13--27 \mathnet{http://mi.mathnet.ru/ufa145} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3432641}