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
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.
second-order equation, decoupling of equations, separation of an equation, submersive system.
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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
\paper Separation of an equation in the system of two second-order ordinary differential equations
\jour Ufimsk. Mat. Zh.
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