Abstract
We perform the group foliation of the system of Lame equations of the classical dynamical theory of elasticity for an infinite subgroup contained in a normal divisor of the main group. The resolving system of this foliation includes the following two classical systems of mathematical physics: the system of equations of vortex-free acoustics and the system of Maxwell equations, which allows one to use wider groups to obtain exact solutions of the Lame equations. We obtain a first-order conformal-invariant system, which describes shear waves in a three-dimensional elastic medium. We also give examples of partially invariant solutions.
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