Stochastic perturbed Fokas-Lenells equation having the polynomial law of self-phase modulation in the presence of spatio-temporal dispersion

The stochastic perturbed Fokas-Lenells equation having cubic-quintic-septic law of self-phase modulation in the presence of spatio-temporal dispersion is considered in this manuscript. The presented model has an important role in studying the complex dynamics of nonlinear wave propagation in diverse physical systems like plasma physics, optical fibers, and fluid dynamics. We reduce the main model to a nonlinear ordinary differential equation utilizing the wave transformation. To derive the analytical solutions for the presented model, we implement the addendum to Kudryashov's method. Thus, we represent the bright and M-shape-like soliton solutions with 3D, contour, and 2D depictions. Besides, the influences of some parameters in the presented model on the soliton character are examined through the 2D plots without noise effect. The results enhance our comprehension of nonlinear wave phenomena and provide valuable insights into designing optical communication systems and strategies for controlling fluid flow.