Abstract The elastic wave propagation in inelastic media gives rise to non-linear equation. We study such a nonlinear two dimensions using Murnaghan model. Lie symmetries, invariant exact solutions and conservation laws the Noether theorem have been found. equation with damping term has dealt partial approach.

To evaluate the earth seismic response due to earthquake effects, ground response analyses are used to predict ground surface motions for development of design response spectra, to compute dynamic stresses and strains for evaluation of liquefaction hazards, and to determine the earthquake induced forces that can lead to instability of earth and earth-retaining structures. Most of the analytical...