Chaotic Structure, Sensitivity Analysis and Dynamics of Solitons to the Nonlinear Fractional Longitudinal Wave Equation

Abstract

The novel family of materials known as magneto-electro-elastic materials has promising potential applications in nanotechnology due to its exceptional energy conversion capabilities. In this work, the different aspects of the fractional nonlinear longitudinal wave equation describing wave phenomena in a magneto electro-elastic circular rod have been studied. The soliton solutions are obtained by advanced methods, namely, (i) generalized Arnous technique (ii) generalized multivariate exponential rational integral function approach. Under certain parameters, this research finds new solitary wave solutions, including bright, singular, combined soliton, and dark solutions. Furthermore, sensitivity analysis and chaotic behavior of this problem is also discussed by the Galilean transformation. Moreover, the 2D, time series, and Poincare mapping as powerful tools for exploring the elusive nature of chaos are presented. The research presented in this study can improve the nonlinear dynamical characteristics of a specific system and validate the efficacy of the used methodologies. Our findings provide useful insights into the intricacy of nonlinear equations, enhancing prior research on the subject through the introduction of innovative techniques and the discovery of a significant number of solutions that have wide-ranging relevance.