Rogue waves for the generalized nonlinear Schrödinger–Maxwell–Bloch system in optical-fiber communication

Abstract

In this letter, a generalized nonlinear Schrödinger–Maxwell–Bloch system is investigated, which can be used to describe the solitons in optical fibers. By virtue of the generalized Darboux transformation, higher-order rogue-wave solutions are derived. Rogue-wave propagation and interaction are analyzed: (1) Complex envelope of the field, q , appears as a bright rogue wave, the measure of the polarization of the resonant medium, p , is a bright-dark rogue wave while the extant of the population inversion, η , is a dark rogue wave; (2) Group velocity inhomogeneity and the linear and Kerr nonlinearity inhomogeneity affect q , p and η more than the other parameters do; (3) Character of the interaction between the propagating field and erbium atoms, the gain or loss term and the linear and Kerr nonlinearity inhomogeneous parameter affect the interaction range of the second-order rogue waves.