Optical Dromion Wave Solutions for the Stochastic Riemann Wave Equation With White Noise Stochastic Term/Random Variable Coefficients and Sensitivity Analysis

This work introduces a nonlinear stochastic Riemann wave equation (SRWE) with particular novel solutions by using the white noise stochastic term. For the considered problem, we have used two computational methods, namely, the auxiliary equation (AE) method and the unified method (UM), for the exact solution and analyzed their various characteristics. With the help of these methods, we have found different forms of solutions, such as singular and bright, hyperbolic, periodic, bright-dark, trigonometric, and exponential soliton solutions, which are plotted in the form of 2D and 3D, respectively. The graphical illustration represents the importance of white noise influencing the exact solution for the considered problem. Numerous fields, including optics, which primarily uses the equation to evaluate the characteristics of light, have made extensive use of it. We can better comprehend the wave–particle duality in quantum physics by using it to characterize the wave function of particles. Studying how sound waves travel through various media is another application of the topic at hand in acoustics.