Analytic solutions and multi-stable chaotic dynamics in perturbed and unperturbed nonlinear electromagnetic wave systems for engineering applications

This paper undertakes a theoretical analytic study of a (3+1)-dimensional NLHSM, thereby generalizing the (2+1)-dimensional NLHSM to three spatial dimensions with a view of capturing rich features in the NL electromagnetic wave systems. From the solutions gained by the IGREM method, a variety of dynamical behaviors, including bifurcation, multi-stable chaos, period, and quasi-period wave structures, are given. Both the cases of perturbation and no perturbation are considered to study the effect of interactions in the various wave phenomena. The complexity of stability and sensitivity of these systems is described through bifurcation analysis, which shows how the system proceeds from stable periodic oscillations to quasi-periodic and chaotic oscillations. The new ideas on the excitation and stabilization of electromagnetic waves in strongly nonlinear media can be useful in engineering, for example, for accurately modeling modern telecommunication systems and controlling waves in plasma physics. The analytic solutions offer a starting point to investigate wave behaviors in higher dimensions, which aids in the creation of new approaches to the management of waves in engineering. Users can gain physical wave behavior access to both simulations and their practical implementation through the generalized model for enhancing electromagnetic wave-based engineering systems. • Analytic solution for perturbed/unperturbed nonlinear electromagnetic wave systems. • The study reveals the multi-stable chaotic dynamics in engineering applications. • Investigates interplay between nonlinear perturbations and soliton-like structures. • Demonstrates how external disturbances influence wave stability.