Chaotic behavior and traveling wave solutions of the fractional stochastic Zakharov system with multiplicative noise in the Stratonovich sense

This study employed the planar dynamics system method to investigate the chaotic behavior and traveling wave solution of the fractional stochastic Zakharov system arising in plasma physics. Through the analysis of the phase portraits, the sensitivity of the dynamic system has been examined and various new exact solutions for traveling waves have been constructed. These obtained solutions are conducive to further understanding the propagation of plasma waves. Furthermore, an analysis of the impact of fractional derivative and random noise on the solutions is done. The chaotic behavior of dynamic systems is examined by time series, Poincae sections, and 2D and 3D phase portraits. Finally, the comparative investigation reveals that the characteristics of the solutions are significantly impacted by both the fractional derivative and random noise. The research methodologies and results are efficacious and can be extended to the exploration of more complex phenomena.