Lie symmetry analysis and conservation laws of non-linear (2+1) elastic wave equation

Abstract

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