Stochastic soliton solutions in birefringent fibers: Analysis of the Biswas–Arshad equation with multiplicative white noise

Abstract

Stochastic partial differential equations are essential in many scientific and engineering disciplines. This study investigates optical stochastic solitons and other exact stochastic solutions in birefringent fibers governed by the Biswas–Arshad equation with multiplicative white noise. By utilizing a new extended hyperbolic function method and generalized exponential rational function method, a diverse range of soliton solutions is obtained. These solutions exhibit either symmetric or anti-symmetric spatial properties, contributing to a deeper understanding of wave dynamics in nonlinear optical systems. Stochastic periodic oscillating nonlinear waves, stochastic kink-wave profiles, stochastic multiple soliton profiles, stochastic singular solutions, stochastic mixed singular solutions, stochastic mixed hyperbolic solutions, stochastic periodic patterns with anti-troughs and anti-peaked crests, stochastic mixed periodic solutions, stochastic mixed complex solitary shock solutions, stochastic mixed shock singular solutions, stochastic mixed trigonometric solutions, and stochastic periodic solutions. Using symbolic computation tools such as Mathematica 14.1 or Maple, the newly derived soliton solutions were validated by substituting them back into the original system. Parameter constraints were analyzed to ensure the existence of these stochastic solutions. Additionally, the selected solutions are illustrated graphically to highlight their physical characteristics and demonstrate the underlying wave dynamics.