Abstract
In this paper, we investigate the nonlinear longitudinal wave equation (LWE) which involves mathematical physics in a magneto-electro-elastic (MEE) circular rod. By three different methods, we found that various forms for exact traveling wave solutions of longitudinal bud equation among an MEE round rod. These new exact and solitary wave solutions are derived in the form of rational, single periodic function, double periodic Jacobian elliptic functions (JEF), especially about Weierstrass elliptic function (WEF). Additionally, certain interesting (3D), (2D) figures represent the LWE provides the corporal information to explain the physically phenomena. By choosing different suitable values of the free parameters, we made some charts and we analyzed these charts to get a lot of valuable information to understand the MEE circular rod. Our work describes the dynamics of the MEE circular rod. Finally, we conclude with some perspectives for our future research work.
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