Abstract
We study the generalized nonlinear Schrödinger Maxwell–Bloch equation describing wave propagation in erbium-doped nonlinear fibers and derive the analytical bright and dark rogue wave and breather solutions under certain parametric conditions. We display the propagation properties of the attained solutions by modulating the relation between maximum effective propagation distance ζm and the parameter ζ0 relating to the excitation type of nonlinear waves. Their controllable behaviors such as fast appearance, postponement, sustainment and annihilation for exponentially dispersion decreasing fiber system have been demonstrated. Additionally, we delineate the longitudinal control of rogue waves. Our results may be useful in understanding and enriching the manipulation of rogue waves in resonant erbium-doped optical fibers.
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