This manuscript studies the stochastic time fraction modified complex Ginzburg–Landau (SFmCGL) model, an essential dynamical nonlinear model for describing the physical nature of how the optical wave soliton behaves and changes over time in a dynamic optical communication system. This study focuses on the bifurcation analysis, chaotic nature, and sensitivity analysis through bifurcation theory and optical soliton solution through the New Jacobian elliptic function (NJEF) method. For the first time, we employ bifurcation theory to examine the influence and importance of current parameters on the proposed system. This analysis elucidates the qualitative behavior of the system, identifying important parameter thresholds at which alterations in solution structure transpire. Second, the chaotic nature and sensitivity analysis are examined with respect to initial conditions. For this investigation, the trigonometric perturbation terms are used and provide the recurrence plot, power spectrum, basin attraction, quasi‐periodic, return map, super‐periodic, and chaotic nature. Additionally, the NJEF method is applied to get the optical soliton solutions for the SFmCGL model. For the parametric values, the bright bell wave, interaction of bell and kink, breather wave, kinky‐periodic wave, and singular bright bell wave solitons are obtained. The literature indicates that bifurcation analysis and chaotic nature have not been conducted for the suggested model, nor has the novel Jacobian Elliptic function approach been applied. These discoveries not only enhance the analytical comprehension of the SFmCGL model but also facilitate the advancement of sophisticated methodologies for investigating nonlinear optical systems. Moreover, this study advances data transmission in the communication process and enables the generation of ultrafast optical pulses by examining the soliton wave propagation in nonlinear diffusive media.
Abd-Elmageed et al. (Thu,) studied this question.