Analysis of optical soliton solutions in weakly nonlocal media to the fractional nonlinear Schrödinger equation in (2+1)–dimension via efficient computational technique

The nonlinear Schrödinger equation (NLSE) is a fundamental model for describing the dynamics of localized, stationary, and pulsating wave structures in nonlinear dispersive media. This study investigates optical soliton solutions of the fractional chiral nonlinear Schrödinger equation (CNLSE) in (2+1)-dimensions using the conformable fractional derivative. The obtained solutions illustrate how wave disturbances evolve over time in weakly stable and unstable media. By employing the extended modified rational expansion (EMRE) method, we derive a diverse set of optical soliton solutions, including kink, anti-kink, bright, dark, peakon, and other solitary wave forms. These solutions provide valuable insights into the underlying physical dynamics of the system. Several solutions are illustrated through two-dimensional, three-dimensional, and contour plots generated via Mathematica. The proposed method is efficient, reliable, and more practical than many existing techniques, making it applicable to other fractional nonlinear evolution equations for obtaining precise analytical solutions.