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

TL;DR

This paper analytically studies a Boussinesq-type equation for longitudinal waves in a magneto-electro-elastic circular rod, finding exact solutions, performing symmetry analysis, and comparing numerical results for different materials.

Contribution

It presents new exact solutions and symmetry reductions for the wave equation, extending previous work with novel solutions and detailed numerical analysis.

Findings

Existence of exact solitary wave solutions.

Identification of new solutions not previously reported.

Numerical results on phase velocity for various materials.

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.