Investigating Chaos and Exact Solutions in Electromagnetic Wave Dynamics Governed by the Time-Fractional Drinfel’d–Sokolov–Wilson Equation

Nonlinear electromagnetic wave propagation in complex plasma environments has attracted considerable attention due to its important applications in nonlinear optics, plasma physics, space science, and communication technologies. In the present study, a time-fractional Drinfel’d–Sokolov–Wilson equation (DSWE) is investigated under the influence of electromagnetic wave perturbations. The fractional-order formulation incorporates memory and hereditary effects, providing a more realistic description of wave propagation in nonlinear dispersive media. By employing an appropriate fractional traveling-wave transformation, the governing nonlinear fractional partial differential equation is reduced to a nonlinear ordinary differential equation. Exact solitary wave solutions are subsequently constructed using the G′G2-expansion technique. Furthermore, the nonlinear dynamical behavior of the reduced system is examined through phase portraits, bifurcation diagrams, Lyapunov exponents, sensitivity analysis, and multistability investigations. Particular attention is devoted to understanding the emergence of chaotic dynamics induced by electromagnetic wave effects and fractional-order interactions. The obtained results reveal that the fractional-order parameter significantly influences the stability, propagation characteristics, and dynamical evolution of nonlinear wave structures. The coexistence of multiple attractors, transitions between stable states, and chaotic regimes is identified for various parameter configurations. These findings provide deeper insight into the complex dynamics governed by the time-fractional DSWE and contribute to the understanding of nonlinear electromagnetic wave propagation in plasma and other nonlinear dispersive media.