Characteristics of New Stochastic Solitonic Solutions for the Chiral Type of Nonlinear Schrödinger Equation

The Wiener process was used to explore the (2 + 1)-dimensional chiral nonlinear Schrödinger equation (CNLSE). This model outlines the energy characteristics of quantum physics’ fractional Hall effect edge states. The sine-Gordon expansion technique (SGET) was implemented to extract stochastic solutions for the CNLSE through multiplicative noise effects. This method accurately described a variety of solitary behaviors, including bright solitons, dark periodic envelopes, solitonic forms, and dissipative and dissipative–soliton-like waves, showing how the solutions changed as the values of the studied system’s physical parameters were changed. The stochastic parameter was shown to affect the damping, growth, and conversion effects on the bright (dark) envelope and shock-forced oscillatory wave energy, amplitudes, and frequencies. In addition, the intensity of noise resulted in enormous periodic envelope stochastic structures and shock-forced oscillatory behaviors. The proposed technique is applicable to various energy equations in the nonlinear applied sciences.