Visualization of the Impact of Noise of the Closed-Form Solitary Wave Solutions for the Stochastic Zhiber-Shabat Model

Abstract

This paper investigates the stochastic Zhiber-Shabat problem under the multiplicative time noise analytically. The Sardar subequation approach is used to explored the solitons and solitary wave solutions under noise. Different families of solutions are gained in the form of dark soliton, singular soliton, bright soliton, complex dark-bright soliton and mixed form solitons along with mixed trigonometric functions. In mathematical physics, the solutions describe a wide range of physical phenomena including chemical kinetics, nonlinear optics, plasma physics, and quantum field theory. The composition of the results would also be displayed in 3D for a variety of parameters using the most modern scientific tools. Graphical representation of the solution's physical behavior demonstrates that the obtained solutions are generated as periodic soliton wave structures with noise term effects that are singular, dark, bright and complex bright dark. Using 3D, 2D, and contour plots with different noise strengths, we illustrate the characteristics of the nonlinear model. It has been shown that choosing a suitable set of parameters optimizes the visual representation of the physical structures.