Investigation of bifurcation analysis and soliton solutions to the longitudinal wave equation in a magneto-electro-elastic circular rod

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.& COPY;2023 L & H Scientific Publishing, LLC. All rights reserved.