Quantum analysis of nonlinear optics in Kerr affected saturable nonlinear media and multiplicative noise: a path to new discoveries

Solitons are characterized by their ability to maintain their shape and velocity as they propagate through a medium, and are also known for their stability against mutual collisions. However, it is crucial to investigate the behavior of nonlinear partial differential equations under random environmental conditions, as this has important implications for a wide range of fields and applications. In this study, the stochastic soliton solutions of the saturable nonlinear Schrödinger equation are found using extended generalized Riccati equation mapping method. To our knowledge, the stochastic solitary wave solutions we have obtained are new in the literature. The discovery of these new solutions is of great importance due to the widespread use of the nonlinear Schrödinger equation in fields such as hydrodynamics, nonlinear optics, and nuclear physics. These solutions exhibit a combination of random behavior and soliton structures that differ from one another. This is an exciting development with potential implications for fields such as physics, engineering, and mathematics. The availability of these solutions provides researchers with a valuable tool to better understand and explain a variety of captivating physical phenomenon. To visualize the behavior of the stochastic soliton solutions, 3D and contour graphs are displayed using Matlab in graphical representation section.