On the new wave behavior of the Magneto-Electro-Elastic(MEE) circular rod longitudinal wave equation

Abstract

The analytical solution of the longitudinal wave equation in the MEE circularrod is analyzed by the powerful sine-Gordon expansion method. Sine - Gordonexpansion is based on the well-known wave transformation and sine - Gordonequation. In the longitudinal wave equation in mathematical physics, the trans-verse Poisson MEE circular rod is caused by the dispersion. Some solutionswith complex, hyperbolic and trigonometric functions have been successfullyimplemented. Numerical simulations of all solutions are given by selecting theappropriate parameter values. The physical meaning of the analytical solutionexplaining some practical physical problems is given.