Selection of solitons coinciding the numerical solutions for uniquely solvable physical problems: A comparative study for the nonlinear stochastic Gross-Pitaevskii equation in dispersive media

In this study, the Gross-Pitaevskii equation perturbed with multiplicative time noise is under consideration numerically and analytically. The NLSE is a universal governing model that helps in evolution of complex fields that are used in dispersive media. For the numerical solution, we used the stochastic forward Euler (SFE) scheme. To find the exact solutions, we chose the techniques namely phi 6-model expansion. For the analysis of the proposed scheme, we checked the stability of the scheme with the help of Von-Neumann criteria and the consistency of the scheme with the mean of Ito's sense. The exact solutions of the model are constructed successfully in the Jacobi elliptic function in the form of trigonometric and hyperbolic functions. Last, we compared the graphical behavior of the proposed scheme with some exact solutions by using the unique selection of initial and boundary conditions. The plots are constructed in the form of 3D, line, and contour representation by choosing the different values of parameters.