On the novel nonlinear propagating waves in stochastic dispersive mode

The solutions of the nonlinear Schrödinger equations (NLSEs) predict the presence of consistent, novel and applicable existences including solitonic localized structures, rouge forms and shocks that propagate based on of physical parameters. The NLSEs with stochastic characteristics predict the anticipated nonlinear process generating decay or forcing in various wave applications. In this work, we discuss the NLSE via noise in Itô sense. New soliton-like, periodic waves and shocks solutions are presented in this study. The presented stochastic structures become crucial in the restricted relationship between the model's nonlinearity, dispersion, and dissipative impacts. These stochastic structures generated changes in frequencies and density structures via noise term. It was observed that noise effects might alter the wave characteristics, thereby producing unprecedented physical and astrophysical densities.