With the help of a group foliation a first-order system (RL) is obtained equivalent to Lame equations of the dynamical theory of elasticity. System (RL) includes the following two classical systems of mathematical physics: the system of equations of vortex-free acoustics and the system of Maxwell equations. The structure of the invariant solutions and some partially invariant solutions of the system (RL) are investigated. Friedrichs t-hyperbolic symmetric evolutionary systems equivalent to wave equations with two and three space variables are found to equivalence transformations. A conformal-invariant Friedrichs t-hyperbolic symmetric evolutionary system is obtained, which describes shear waves in a three-dimensional elastic medium. Using complex variables, this system is written in the form convenient for obtaining its exact solutions. Some partially invariant solutions are also obtained.
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