Dynamics of soliton solutions in the chiral nonlinear Schrödinger equations

In this study, the $(1+1)$- and $(2+1)$-dimensional Chiral nonlinear Schrödinger equations are investigated. These equations describe the edge states of the fractional quantum hall effect. We successfully acquired dark and bright soliton solutions to these equations by using the sine-Gordon expansion method. The constraint conditions for the existence of valid soliton are given. We present the numerical simulations to some of the obtained solutions under the choice of suitable parameters.