Chiral Nonlinear Schrödinger Equation in (1+2) dimensions and Simplest Equation Technique

Abstract

In this study, we employ two efficient analytical techniques the simplest equation ap proach and the tanh-coth method to investigate the (1+2) dimensional non-linear chiral Schrödinger equation. In condensed matter physics and nonlinear optics, this equation is essential, describing the propagation of light in materials with significant nonlin earities 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 under standing 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 follow ing section and conditions enabling various solutions, including exponential, singular and periodic solitons. This work shows how adding nonlinearity affects Schrödinger’s system. It helps us understand chiral effects in nonlinear systems better and opens up opportunities for more research in this area.