Chiral bright, dark and singular Solitons for the Nonlinear Schrödinger Equation in (1+2) Dimensions

In this study, we employ two efficient analytical techniques, the simplest equation approach and the tanh-coth method to investigate the (1+2) dimensional nonlinear chiral Schrödinger’s equation. In condensed matter physics and nonlinear optics, this equation is essential, describing the propagation of light in materials with significant nonlinearities and chiral properties. By employing the simplest equation method, we derive exact solutions that reveal the complex relationship between nonlinearity and chirality. Additionally, the tanh-coth method yields exact soliton solutions, enhancing our understanding of soliton dynamics in chiral media. Our results provide new insights into the behavior of nonlinear waves in (1+2) dimensions and demonstrate the effectiveness of these methods in solving complex nonlinear equations. We present analytical solutions for bright and dark solitons. We also discuss the variables of the system in the following section and conditions enabling various solutions, including singular and periodic solitons.