A group analysis of the equations of the dynamic transversely isotropic elastic model

Group foliation of the system of equations of motion of a transversely isotropic elastic model of geomaterials, satisfying the Gassmann conditions, is carried out. A linear system of first-order differential equations is obtained, equivalent to the equations of this model. A number of theorems describing its properties are proved. A fundamental Lie transformation and an optimum system of its subgroups are obtained, which enable all the invariant, partially invariant and differentially invariant submodels of the dynamic model of a transversely isotropic elastic medium to be obtained. Some exact solutions are derived and their physical meaning is indicated.