Dynamics of optical solitons in the (2 + 1)-dimensional chiral nonlinear Schrödinger equation

Abstract

The [Formula: see text]-dimensional chiral nonlinear Schrödinger equation (CNLSE), which specifies the edge states of the Hall effect, is presented in this study. A complicated transformation is performed, and the bifurcation conditions are determined using the theory of planar dynamical systems. The phase pictures of the system are then produced using quantitative analysis in order to predict the family of solutions which can be found for the equation studied. It is important to note that this prediction is usually not made. The qualities of phase pictures are then used to obtain the exact solutions. As a result, this model produces some bright solitons, dark solitons and periodic wave solitons. Some of the solutions are graphically depicted in three dimensions (3D) using Matlab software to aid comprehension, and they play an important part in the creation of realistic Quantum Hall effects when Chiral excitations are known to occur. The method applied in this paper is simple and does not need an ansatz to predict the solutions as in the literature.