Description of soliton and lump solutions to [formula omitted]-truncated stochastic Biswas–Arshed model in optical communication

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This article negotiates the investigation of optical stochastic solitons and other exact stochastic solutions with the fractional stochastic Biswas–Arshed equation (FSBAE) describing the multiplicative white noise of optical signal propagation in birefringent fibers using the modified F-expansion method and Hirota Bilinear method. In order to manage this model, we used Itô calculus. After utilizing the aforementioned techniques and computational software, different stochastic solitary wave solutions are retrieved, including dark, bright, periodic, singular, hyperbolic, rational, combo, and trigonometric function solutions. Additionally, we also investigate several wave solutions, such as the cross-kink rational wave solution, the homoclinic breather wave solution, and M-shaped rational solution. To examine the different kinds of solitons and their dynamical behaviors, the solutions have been simulated by graphs. The discovered solutions are essential for illuminating the wave dynamics in diverse models. The obtained stochastic solitary wave solutions may be crucial in nonlinear science and engineering fields. It is impressive to see that the chosen methodologies are simple, appropriate, and effective scientific tools for determining stochastic solitary wave solutions for nonlinear engineering models (NLEMs). This is the first investigation into the lump solutions of the FSBA equation with multiplicative white noise, and the findings show how optical solitons propagate in nonlinear optics.