We consider in this paper the stochastic nonlinear Schrödinger equation forced by multiplicative noise in the Itô sense. We use two different methods as sine-cosine method and Riccati-Bernoulli sub-ODE method to obtain new rational, trigonometric and hyperbolic stochastic solutions. These stochastic solutions are of a qualitatively distinct nature based on the parameters. Moreover, the effect of the multiplicative noise on the solutions of nonlinear Schrödinger equation will be discussed. Finally, two and three-dimensional graphs for some solutions have been given to support our analysis.

In this paper we introduce a robust and accurate solver in order to solve various classes of nonlinear partial differential equations. This solver gives the closed formula for the solutions. Within this respect, a solver is developed to accurately resolve and represent the complete wave structure of the nonlinear partial differential equations. To verify this solver, the two applications are introduced. The obtained solutions may be applicable for some new observations in physics, fluid mechanics, biology, engineering, economy, astrophysics, meteorological topics, gravitational collapse and laser technology. The theoretical study and obtained solutions reported illustrating that the proposed solver efficient and adequate. The shape for the obtained solutions are illustrated via 2D and 3D plots for suitable values of the free parameters.

The exact new solutions are given in the form of rational, exponential, trigonometric and hyperbolic forms in which some of them are new and realistic for Schrödinger equation. Numeral studies have been reveals that the obtained solutions may be applicable for some physical environments, such as plasma fluids and fiber communications. The computational study and obtained conclusions reported that the offered methods are pretentious, robust and influential in applications of voyager storm analysis, observations of space plasmas and in optical fibers.