Solitonic wave structures and stability analysis for the coupled (2 + 1)-dimensional nonlinear Schrodinger-Maxwell-Bloch system in an erbium-doped fibre

This study addresses the coupled (2 + 1)-dimensional nonlinear Schrödinger-Maxwell-Bloch (NLS–MB) system, which represents the optical pulse distribution in an erbium-doped fibre. The primary goal is to construct explicit soliton solutions and analyze their dynamical characteristics. Based on the ansatz method, its bright, dark and singular soliton solutions are constructed under some constraint conditions. In addition, by using the unified Riccati equation expansion method, the extended Kudryashov’s method and the modified exp-function method, some other soliton solutions and periodic solutions are formally derived. The solutions obtained from the analytical approaches were systematically compared to highlight the relative efficiency of each method in addressing the nonlinear model and to validate the robustness of the derived results. Graphical analysis of obtained results are presented to get the better understanding of their dynamical behaviours. Further, the modulation instability is analyzed based on the standard linear stability analysis. The consequence of numerous incident powers on the instability gain spectrum is illustrated graphically. The novelty of this work lies in the combination of multiple analytical methods to uncover new solution types and in providing a comprehensive study of their stability and modulational characteristics, which enhances the understanding of pulse dynamics in nonlinear optical fibers.