Abstract
This study, analyzed the explicit solitary wave soliton for the stochastic resonance nonlinear Schrödinger equation under the Brownian motion. The Schrödinger equations are mostly used to describe how light moves via planar wave guides and nonlinear optical fibres. Analytical technique is applied to gained the various solitary waves and soliton solutions for the resonance nonlinear Schrödinger equation namely, generalized exponential rational function method. This approach is used to find several new trigonometric, exponential, and hyperbolic solutions under the noise. This method is provided us the soliton solutions for nonlinear models that is a computed using an efficient, accurate, capable, and trustworthy method. Furthermore, by varying the parameters, a few graphs of the developed solutions are shown to illustrate the physical setup of stochastic solutions. We anticipate that the obtained results will have significant potential applications in quantum mechanics, magneto-electrodynamics, optical fibres, and heavy ion collisions. Moreover, using the Galilean transformation, the dynamical system of the governing equation is obtained, and the theory of the planar dynamical system is used to carry out its sensitivity, chaotic and bifurcation. By providing certain two- and three-dimensional phase pictures, the existence of chaotic behaviors of the resonance nonlinear Schrödinger equation is examined by taking into account a perturbed term in the resulting dynamical system.