Group invariant solutions of wave propagation in phononic materials based on the reduced micromorphic model via optimal system of Lie subalgebra

Abstract

In this paper the system of equations arising from a simplified micromorphic model is studied using the Lie symmetry approach. The advantage of this approach is that is provides exact invariant solutions rather than numerical or approximate ones reported in the literature in earlier studies. We obtain the Lie point symmetries for the model and the one dimensional optimal system of Lie subalgebras. Using the one-dimensional optimal system, symmetry reductions are performed and some corresponding invariant solutions are found. To illustrate the physical importance of group invariant solutions, 2D, 3D and contour plots are drawn.