Abstract
This paper studies the analytical and semi-analytical wave solutions for the longitudinal wave equation. Moreover, it examines the performance of the modified auxiliary equation method and Adomian decomposition method on this model. This model describes the dispersion in the circular rod that dispersion caused by the transverse Poisson's effect in electro-magneto-elastic. Many explicit wave solutions are found by using the analytical technique. These solutions allow studying the physical properties of this model. The comparison between the analytical and semi-analytical solutions is discussed to show the value of the absolute error between them.