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In this article, the generalised nonlinear Schrödinger–Maxwell–Bloch system is investigated, which describes the propagation of the optical solitons in an optical fibre doped with two-level resonant impurities like erbium with the fourth-order dispersion taken into account. Bilinear forms are derived via the Hirota method, symbolic computation, and the auxiliary function. Bright solitons can be obtained for the complex envelope of the field and the measure of the polarisation for the resonant medium, while the dark ones have been deduced for the extant population inversion. Propagation of the one and two solitons is analysed with the results that the solitons keep their shapes unchanged after the interaction, except for the phase shifts, which means that the interaction is elastic. Velocities of the solitons decrease when the effect of discreteness and higher-order dispersion increases. For the bound-state solitons, which can be formed among the solitons at the same velocity, the period decreases when the effect of discreteness and higher-order dispersion increases.

Soliton Solutions of a Generalised Nonlinear Schrödinger–Maxwell–Bloch System in the Erbium-Doped Optical Fibre