On Stochastic Pure-Cubic Optical Soliton Solutions of Nonlinear Schrödinger Equation Having Power Law of Self-Phase Modulation

Abstract

In this study, we focus on the stochastic pure-cubic optical solitons of the nonlinear Schrödinger equation, characterized by a parabolic law of nonlinearity. The nonlinear Schrödinger equation models are crucial for simulating pulse propagation in optical fibers especially ultrashort pulses. To obtain optical soliton solutions, we employ the effective and well-known the new Kudryashov and the generalized Kudryashov methods. Through these methods, we successfully derive dark, bright, and singular optical soliton solutions. Our findings are illustrated with 2D and 3D graphics for clarity. A significant aspect of our study is the inclusion of stochasticity in the model. We specifically examine the impact of white noise on the solutions. This effect is detailed in the results section, with corresponding graphs. Throughout our research, we did not encounter any restrictive factors that hindered access to the results. Ultimately, considering the growing number of studies on optical fibers, our work stands out by being the first to obtain optical solutions for this specific model and by investigating the influence of stochastic theories on wave behavior.