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Generalized equivalence transformations and group classification of systems of differential equations

Yu. A. Chirkunov

Novosibirsk State Technical University, Novosibirsk, 630092, Russia

Abstract: The notion of generalized equivalence transformations for which the equivalence transformations considered by Ovsyannikov are universal equivalence transformations is introduced for a system of differential equations. An algorithm of the group classification of the system of differential equations with the help of these generalized equivalence transformations is proposed. The efficiency and advantages of this algorithm are demonstrated by examples of equations of gas dynamics and equations of nonlinear longitudinal oscillations of a viscoelastic bar in the Kelvin model.

Keywords: group classification of systems of differential equations, generalized and universal equivalence transformations, group of equivalences, equations of gas dynamics, nonlocal symmetries.

UDC: 517.9+533.6+539.3

Received: 14.04.2011

 English version: Journal of Applied Mechanics and Technical Physics, 2012, 53:2, 147–155

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