Nonlinear wave dynamics and multistability in engineering electromagnetics: Numerical analysis of perturbed and un-perturbed systems within the Higgs field

The objective of this work is to study the dynamics and multiple stability of electromagnetic waves interacting with the medium affected by the Higgs field, both in disturbed and stable conditions. The numerical analysis uses an enhanced approach known as the improved Generalized Riccati Equation Mapping Method (GREMM), which is suitable for such systems' analysis because of strong, complex behaviors. In this way, one investigates the changes in the wave configurations and stability preferences for different circumstances of perturbation and the impact of the Higgs field. The following set of relations presents stability relations, where depending on the parameter values, the system can be either uni- or bistable, or multistable, displaying more than one stable state. From the phase portraits, it can be seen that the proposed system shows periodic behavior, which tends to the multistability. Particularly, we propagate disturbances that alter the behavior of electromagnetic waves and their coupling with the substratum Higgs field; this gives insight into the nature of wave-particle correlations in that type of physics system. The research emphasizes the importance of shallow nonlinear phenomena and the notion of the Higgs field regarding the nature of electromagnetic waves and their possible usage in various areas, from physics to the domain of advanced engineering. Thus, this study enriches the understanding of nonlinear waves and provides a solid ground for analyzing similar waves in other physical problems.