Journal of Applied Nonlinear Dynamics 12(4) (2023) 767--780 | DOI:10.5890/JAND.2023.12.010

Nisa Çelik, Emrullah Yaşar

Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, 16059 Bursa, Turkey

Abstract

In this study, we examined the nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod of fourth order. Firstly, bifurcation behavior was examined by the help of a planar dynamical system to analyze the bifurcation structures of traveling wave solution forms of the considered equation. All possible phase portraits are exposed with some parameter assignment. Secondly, generalized Kudryashov and auxiliary equation methods were used to investigate the traveling wave solutions for this equation. The solutions of the longitudinal wave equation types as solitary waves, periodic traveling waves, periodic cusp wave solutions are discussed. The existence of these solutions was also demonstrated by bifurcation analysis. The physical properties of these longitudinal waves were trying to be discovered by drawing dynamic analysis of these systematically produced solutions.

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