Propagation of wave insights to the Chiral Schrödinger equation along with bifurcation analysis and diverse optical soliton solutions

In this study, the modified Sardar sub-equation (MSSE) method is capitalized to secure soliton solutions to the ( 1 + 1 ) -dimensional chiral nonlinear Schrödinger (NLS) equation. Chiral soliton propagation in nuclear physics is an extremely attractive field because of its wide applications in communications and ultrafast signal routing systems. Additionally, we perform bifurcation analysis to gain a deeper understanding of the dynamics of the chiral NLS equation. This highlights the complex behavior of the system and exposes the conditions under which various types of bifurcations occur. Additionally, a sensitivity analysis is performed to assess how small changes in initial conditions and parameters influence the solutions, offering valuable perspectives on the stability and dependability of the acquired solutions. By employing the above-mentioned methodology, we derive a variety of exact solutions, including periodic, singular, dark, bright, mixed trigonometric, exponential, hyperbolic, and rational wave solutions. The study’s findings advance our theoretical knowledge of chiral NLS equations and have potential applications in optical communication and related fields.