Abstract
The analytical solution of the longitudinal wave equation in the MEE circular rod is analyzed by the powerful sine-Gordon expansion method. Sine - Gordon expansion is based on the well-known wave transformation and sine - Gordon equation. In the longitudinal wave equation in mathematical physics, the transverse Poisson MEE circular rod is caused by the dispersion. Some solutions with complex, hyperbolic and trigonometric functions have been successfully implemented. Numerical simulations of all solutions are given by selecting the appropriate parameter values. The physical meaning of the analytical solution explaining some practical physical problems is given.
Highlights
Innovative analytical new solutions for non-linear evolution equations (NEEs) has very important role in area of non-linear physics
By utilizing the sine-Gordon extension method with the help of symbolic mathematical software, we investigated the solution of the magneto-electro-elastic circular rod longitudinal wave equation
All solutions obtained in this study validate wave equations in magneto-electro-elastic circular rod and we examine this using the same procedure as symbolic mathematical software
Summary
Innovative analytical new solutions for non-linear evolution equations (NEEs) has very important role in area of non-linear physics. Many more analytical techniques have been designed and used in obtaining analytical solutions of different NLEs [11,12,13,14,15,16,17,18,19,20,21,22]. The powerful sine-Gordon expansion method (SGEM) [31, 32] was used to find some new solution methods to the longitudinal wave equation of the magneto-electro-elastic (MEE) circular rod [33] in this study. To the longitudinal wave equation in magnetoelectro-elastic MEE circular rod, like the improved (G′/G)-expansion method [35], the functional variable method [36],the ansatz method [37], etc
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