Abstract
This paper presented exact solutions and stability analysis to the nonlinear longitudinal wave equation (NLLWE) in a magneto electro-elastic (MEE) circular rod. The new generalized exponential rational function method (GERFM) has been applied for finding the exact solutions of NLLWE in MEE circular rod. It has the capacity to generate many types of solutions in different form. Therefore, it is effective in extracting new types of solutions in other nonlinear partial differential equations (NLPDEs) that commonly model applications in engineering, mathematical physics. Furthermore, some 2D, 3D graphs are obtained to understand the physical phenomena of this longitudinal wave equation and the stability of governing equation is investigated.