The random noise modulations on the nonlinear Chiral Schrödinger structures

In this paper, we consider the Chiral nonlinear Schödinger equation (CNLSE), where the multiplicative noises term varies arbitrarily over time. This equation defines several edge states of Hall effect characteristics in quantum physics applications. We apply the sine-Gordon expansion method to produce some new stochastic solutions for the CNLSE. Some solitary and dissipative solutions were obtained in the form of rational, envelope and shock structures. We demonstrate how the multiplicative noise and model parameters affects the way the solutions behave. We provide some configurations for the both deterministic and stochastic solutions to illustrate their behaviour. It is known that noise dominates envelope growing, damping, and all wave propagation. As it is achieved, the results presented here are crucial to the development of quantum physics. The proposed methodology can be developed to solve more complex problems in applied science.