The effect of multiplicative noise on the exact solutions of nonlinear Schrödinger equation

: We consider in this paper the stochastic nonlinear Schr¨odinger equation forced by multiplicative noise in the Itˆo sense. We use two di ff erent 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 e ff ect of the multiplicative noise on the solutions of nonlinear Schr¨odinger equation will be discussed. Finally, two and three-dimensional graphs for some solutions have been given to support our analysis.