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 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.

An Analytical Approach to an Elastic Circular Rod Equation

“…( 1), the reduced equation is solved i.e. the original equation is not solved [8,12,13,17,18,19]. Using the novel balancing principle for non-power-law non-linearity, Eq.…”

“…Although, no matter how thin the rod is, it is always assumed three-dimensional, when the rod diameter is much smaller than the axial length scale, it is reasonable to expect that approximate one-dimensional equations (rod equations) can give a good description of the motion of the rod. Many modifications of rod equations are seen in the literature and these equations ignore many properties of rod and constraining terms [8,12,13,17,18,19]. In this work, the considered rod equation was not studied before in the literature and it contains physical and chemical properties of the rod.…”

“…In the literature, solitary wave solutions of the Eq. (1.1) are obtained for n = 2 and n = 3 by simplicity [17,19,20]. Generally, the ansatz is determined after reducing and integrating the Eq.…”

Construction of Soliton Solutions for Chaffee-Infante Equation

“…Recently, various methods have been developed by many researchers for NLEEs, which have many uses in mathematics and physics (Akram and Mahak 2018, Alam and Akbar 2014, Qawasmeh and Alquran 2014, Taghizadeh 2012, Tasbozan et al 2016, Tuluce Demiray et al 2015, Tuluce Demiray and Bulut 2017a, Tuluce Demiray and Bulut 2017b, Tuluce Demiray and Bulut 2019, Wazwaz 2005, Durur et al 2020, Duran 2021. In this study, we will use the sine-Gordon expansion method (SGEM), which is one of the widely used methods to find the solutions of NLEEs (Bulut et al 2016, İlhan et al 2020, Kumar et al 2017. SGEM has been created from traveling wave transformation and sine-Gordon equation (Yan and Zhang 1999).…”

Modeling of Dark Solitons for Nonlinear Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod

“…where g is the linear longitudinal wave velocity and q is the dispersion parameter for a magneto-electroelastic circular rod, all of which depend on the material property and geometry [40].…”