Rogue-wave interaction for a higher-order nonlinear Schrödinger–Maxwell–Bloch system in the optical-fiber communication

In this paper, a higher-order nonlinear Schrödinger–Maxwell–Bloch system in the optical-fiber communication is investigated. By virtue of the generalized Darboux transformation, higher-order rogue-wave solutions are derived. Wave propagation and interaction are analyzed: (1) The frequency affects the number of troughs, type and propagation direction of rogue waves for the polarization of the resonant medium and extant population inversion, while the frequency has no influence on the module for the complex envelope of the field. (2) The frequency affects the type of the higher-order rogue-wave interaction. Second- and third-order rogue-wave head-on interactions are presented, with the propagation direction of each rogue wave unvaried after the interaction.