On the optical soliton structures in the magneto electro-elastic circular rod modeled by nonlinear dynamical longitudinal wave equation

In this article, we focus on securing the different soliton and other solutions in the magneto electro-elastic (MEE) circular rod. The abundant solutions of the nonlinear longitudinal wave equation (NLWE) with dispersion caused by the transverse Poisson's effect in a long MEE circular rod are obtained using the modified Sardar sub-equation method (MSSEM). The study of optical solitons' nonlinear dynamics in MEE media (such as sensors, actuators, and controllers) has piqued researchers' interest. The wave structures in different kinds of solitons, such as bright, dark, singular, bright-dark, bright-singular, complex, and combined, are extracted. In addition, hyperbolic, trigonometric, exponential type and periodic solutions are guaranteed. Nonlinear partial differential equations (NLPDEs) are well-explained by the applied technique since it offers previously derived solutions and also extracts new exact solutions by incorporating the results of multiple procedures. Moreover, in explaining the physical representation of certain solutions, we also plot 3D, 2D, and contour graphs using the corresponding parameter values. This paper's findings can enhance the nonlinear dynamical behavior of a given system and demonstrate the efficacy of the employed methodology. We believe that a large number of specialists in engineering models will benefit from this research. The results indicate that the employed algorithm is effective, swift, concise, and applicable to complex systems.

Automated summary

This article focuses on securing different soliton and other solutions in the magneto electro-elastic circular rod. Abundant solutions for the nonlinear longitudinal wave equation with dispersion in a long MEE circular rod are obtained using the modified Sardar sub-equation method. The findings of this paper enhance the nonlinear dynamical behavior of a given system and demonstrate the efficacy of the employed methodology.