Exact Solutions and Symmetry Analysis of a Boussinesq type Equation for Longitudinal Waves through a Magneto-Electro-Elastic Circular Rod

Abstract

In this work the longitudinal wave equation through magneto-electro-elastic circular rod is studied analytically. Painlev\'e test is performed to check integrability of the equation. Exact solitary wave solutions are found by homogeneous balance method and Tanh method and are plotted using suitable values of physical parameters. A similar solution to an earlier related work [17, 20] is obtained. However we have obtained a new solution as well. Lie symmetry analysis has been done and similarity reduction of the equation is presented. Numerical results related to phase velocity etc for different materials has been derived and compared.