Localized excitations for a (2+1)-dimensional Hirota–Maxwell–Bloch system in an erbium-doped optical fiber

Under investigation is the (2+1)-dimensional Hirota–Maxwell–Bloch system which models ultrashort pulse propagation in erbium-doped optical fibers by coupling nonlinear dispersion with resonant light–matter interactions. Using a generalized Darboux transformation, we construct new classes of localized excitations that had not been previously reported, including higher-order degenerate solitons, degenerate lump chains, and rational lump solutions. These structures arise from the intricate balance and interplay between the dispersion, nonlinearity, and resonant energy exchange within the system. The degenerate solitons display diverse profiles such as bright, dark, M-shaped, and W-shaped structures, while higher-order solutions reveal non-reciprocal energy flow, polarization bimodality, and even vortex-type topological phases. For lump chains, three distinct regimes generate eye-shaped, beak-shaped, and line-shaped patterns with rich interaction behaviors. Rational lump solutions further exhibit inclined peak geometries and multi-peak interactions governed by quadratic spatial forms. These findings close a theoretical gap in multidimensional HMB dynamics and offer new insights into nonlinear energy localization and wave interactions, with potential implications for ultrafast optics and coherent wave phenomena in fluid and plasma systems.