Generalized equivalence transformations and group classification of systems of differential equations

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.