New solitary optical solutions for the NLSE with δ-potential through Brownian process

The Brownian motion is the most important stochastic process in dispersive nature. In this article, the robust solver approach is utilized to extract some new optical soliton solutions to the cubic nonlinear Schrödinger equation with δ-potential (δ-NLSE) via Brownian motion process. Namely, we introduce some new stochastic solutions with functional physical parameters. The presented solutions are novel and very beneficial to describe some physical phenomena in optical fiber communications. We investigate the influence of the noise term on the dynamical behavior of the acquired solutions. Some graphs of selected solutions are introduced to exhibit the dynamical behavior of these solutions. Our results show the accuracy and efficiency of the proposed solver in order to solve many other models arising in applied science.