Rogue-wave interaction of the generalized variable-coefficient Hirota–Maxwell–Bloch system in fiber optics

In this paper, a generalized variable-coefficient Hirota–Maxwell–Bloch system is investigated, which can describe the propagation of optical solitons in an erbium-doped optical fiber. Higher-step generalized Darboux transformation and rogue-wave solutions are obtained. Rogue-wave interaction is analyzed as follows: (1) Variable coefficients in the system affect the shape, background and number of the wave crests and troughs of the first-step rogue waves for the modulus of the normalized slowly varying amplitude of the complex pulse envelope, modulus of the measure of the polarization of the resonant medium and extant population inversion; (2) Variable coefficients in the system affect the shape, background and number of the wave crests and troughs of the second-step rogue-wave interaction. Those phenomena can not be attained through the existing Hirota–Maxwell–Bloch system.