Propagation properties of soliton solutions under the influence of higher order effects in erbium doped fibers

•The Akhmediev breathers, Ma-breathers for the Hirota–Maxwell–Bloch system.•Bound solitons, two-breathers and localized solutions have been derived.•Dynamic features of those solitons have been analyzed.

Under investigation in this paper is the Hirota–Maxwell–Bloch system which governs the propagation of optical solitons in nonlinear erbium doped fibers with higher order effects. By virtue of the Darboux transformation, the Akhmediev breathers, Ma-breathers, localized solitons, bound solitons, two-breathers and localized solutions are generated for the Hirota–Maxwell–Bloch system. Considering the influences of higher order effects, propagation properties of the breathers, modulation instability conditions for the Akhmediev breathers and interaction scenarios between bound solitons and two-breather solutions are discussed.