Analytical study of solitons in magneto-electro-elastic circular rod

A family of solutions of the time–space fractional longitudinal wave equation

“…In recent years, the study of exact solutions in magnetoelectro-elastic media (such as sensors, actuators and controllers) has attracted more and more attention from mathematicians and physicists [1][2][3][4]. As everyone knows, the governing equation that describes the propagation of solitons through magneto-electro-elastic media is modeled by a longitudinal wave equation of the form [1]…”

“…where c 0 is the linear longitudinal velocity of a magnetoelectro-elastic circular rod and N > 0 is the dispersion parameter [1]. It is well known that equation (1) has been studied by many researchers, with solutions such as the one-soliton and peaked solitary wave solutions [2], the bright and singular soliton solutions [3], the hyperbolic function solitary wave solutions and plane wave solutions [4]. In addition, equation (1) can be reduced to the Boussinesq equation in the case of traveling wave solutions, which have N-soliton solutions [5].…”

Magneto-Elektro-Elastik Çubuk Modelinin F Açılım Metodu ile Tam Çözümleri

“…, = − alarak gezen dalga hipotezi ve ′ ⁄ açılım metodu [21], sin-cos fonksiyon metodu ve rasyonel sin-cos fonksiyon metodu [22], genişletilmiş deneme denklem dönüşüm metodu ve genişletilmiş doğrudan cebirsel denklem metodu [23], genişletilmiş deneme denklem metodu [24] biçimindedir.…”

New Optical Solitons of the Longitudinal Wave Equation in a Magnetoelectro-Elastic Circular Rod

“…In a similar study, Yang and Xu [45] adopted the ansatz method to construct the 1-soliton solution and peaked solitary wave solutions of the nonlinear longitudinal wave equation in a magnetoelectroelastic circular rod. Xue and coworkers [46] applied the Jacobi elliptic function expansion method for the exact solution of the NLWE in a magnetoelectro-elastic circular rod, and Zhou [47] solved the nonlinear longitudinal wave equation in a magnetoelectro-elastic circular rod via (G /G)-expansion method and traveling wave hypothesis. The rest of this study is structured according to the following sections.…”