Solitary wave solutions of chiral nonlinear Schrödinger equations

Abstract

This paper presents the (1+1)-dimensional chiral nonlinear Schrödinger equation (1DCNLSE) and (2+1)-dimensional chiral nonlinear Schrödinger equation (2DCNLSE) that define the edge states of the fractional quantum hall effect. In this paper, we implement the Riccati–Bernoulli sub-ODE method in reporting the solutions of these two nonlinear physical models. As a result of this, some singular periodic waves, dark and singular optical soliton solutions are generated for these models. Some of the acquired solutions are illustrated by three-dimensional (3D) and two-dimensional (2D) graphs utilizing suitable values of the parameters with the help of the MAPLE software to demonstrate the importance in the real-world of the presented equations.