EXACT SOLUTIONS OF THE (1+1)-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION VIA A NOVEL ANALYTICAL APPROACH

This study investigates the (1+1)-dimensional chiral nonlinear Schrödinger (NLS) equation, crucial in nuclear physics for modeling chiral soliton propagation. The Extended Direct Algebraic Method (EDAM) is employed to derive a diverse range of exact solutions, including periodic, solitary, dark, bright, mixed trigonometric, hyperbolic, and rational wave solutions. These solutions provide valuable insights into the complex behavior of chiral nonlinear systems. A sensitivity analysis assesses the impact of initial condition and parameter perturbations on solution stability, highlighting the robustness and reliability of the obtained solutions. The findings contribute significantly to understanding chiral NLS equations, with potential applications in Ultrafast signal routing systems, Optical communication, Nonlinear optics, Condensed matter physics. This research advances theoretical knowledge and provides a solid foundation for future studies on chiral nonlinear systems. The exact solutions obtained can be used to model and analyze complex phenomena in various fields, demonstrating the versatility and efficacy of the mEDAM technique.