Characteristics of stochastic solutions for the chiral NLSE through Brownian motion process

Abstract

In this work, we produce some new stochastic chiral solitons for the chiral nonlinear Schrödinger equation through Brownian motion process. Specifically, we use the unified approach to produce these soliton solutions. These solutions are so important in quantum mechanics, optical fiber communication, heat transfer, applications of energy, etc. These solutions behave in qualitatively distinct structural ways, based on physical coefficients parameters and the noise parameter. The results of the solitary structures of this system agree well with the properties of the nonlinear Schrödinger systems used to investigate dispersive modes and higher-order chiral systems. We introduce some plots for the deterministic and stochastic cases in order to show the behavior of waves in both cases. Namely, we used Matlab 18 to create comprehensive configurations to highlight the physical dynamical description of the solutions as well as provide further information. The dominance of the noise term in all wave conversion, growth, and damping of envelopes and shocks has been verified. Finally, our analysis can be outspread to several equations arising in natural science.