Impact of Brownian motion on the optical soliton solutions for the three component nonlinear Schrödinger equation

In this manuscript, the three-component nonlinear stochastic Schrö dinger equation under the effects of Brownian motion in the Stratonovich sense is examined here. The different types of exact optical soliton solutions are explored under the noise effects. The propagation of an optical pulse in a birefringent optical fiber is described by the three nonlinear complex models. A system of coupled nonlinear Schrödinger equations can be used to characterize the propagation of light in birefringent optical fibers. The interactions between the various polarization modes of the optical field are taken into account by the equations for a three-component system. In a three-component nonlinear Schr ödinger (NLS) equation, the three-wave mixing effect typically arises from cross-phase modulation (XPM) and four-wave mixing (FWM) terms. These terms describe interactions between the three wave components. A well-known mathematical technique is used namely as generalized Riccati equation mapping method. The different types of dark, singular, combined, and solitary wave solutions are constructed. Moreover, the effect of noise is visualized on these optical solitons. To show the stability of our results we have explored one more method namely as modified auxiliary equation method, which provided us only hyperbolic, trigonometric and rational solitons. The effect of noise is shown via simulations in the 3D, 2D, and corresponding contours. The computational software Mathematica11.1 is used to construct these solutions, and their verifications and to draw the plots as well under the effect of noise.