New bright and dark stochastic optical solitons related to an eighth-order NLSE in the presence of higher order polynomial nonlinearity

The main objective of this research is to investigates the intricate realm of high stochastic solitons. The underlying model is an eighth-order nonlinear Schrödinger equation, considering the effects of spatio-temporal dispersion with elevated polynomial nonlinearity and multiplicative white noise. The influence of these factors on soliton’s behavior is investigated using Itô calculus. To explore the impact of multiplicative white noise on the governing model more clearly, both bright and dark soliton profiles are generated that are associated with the given equation. Two valid techniques, the Sine-Gordon expansion method and modified sub-equation method that are widely employed in nonlinear dynamics and soliton theory, are utilized to create these solitonic shapes in the presence of white noise. It has been noted that the phase component of the solitons contains the white noise, examining the full spectrum of soliton solutions. These techniques offer a versatile approach to collecting various soliton solutions in this field. Using both 3D and 2D visualization tools, solutions in clear graphical representations are provided. This one-of-a-kind combination of problem and methodology has led to the discovery of a plethora of novel soliton solutions and their accompanying behaviors.