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

In this work the longitudinal wave equation through magneto-electro-elastic circular rod is studied analytically. Painlevé test performed to check integrability of equation. Exact solitary solutions are found by homogeneous balance method and Tanh plotted using suitable values physical parameters. A solution similar an earlier related (Xue et al. in Smart Mater Struct 20:105010, 2011; Ma Int J Comput Sci Issues 10 (1): 62–68, 2013) obtained. However a new obtained as well. Lie symmetry analysis has been done similarity reduction presented. Dependence on velocity dispersion parameter transverse Poisson effect numerically. Numerical results phase etc for different materials have derived compared.