Rogue waves in a resonant erbium-doped fiber system with higher-order effects

摘要

We mainly investigate a coupled system of the generalized nonlinearSchr\"odinger equation and the Maxwell-Bloch equations which describes the wavepropagation in an erbium-doped nonlinear fiber with higher-order effectsincluding the forth-order dispersion and quintic non-Kerr nonlinearity. Wederive the one-fold Darbox transformation of this system and construct thedeterminant representation of the $n$-fold Darboux transformation. Then thedeterminant representation of the $n$th new solutions $(E^{[n]},\, p^{[n]},\,\eta^{[n]})$ which were generated from the known seed solutions $(E, \, p, \,\eta)$ is established through the $n$-fold Darboux transformation. Thesolutions $(E^{[n]},\, p^{[n]},\, \eta^{[n]})$ provide the bright and darkbreather solutions of this system. Furthermore, we construct the determinantrepresentation of the $n$th-order bright and dark rogue waves by Taylorexpansions and also discuss the hybrid solutions which are the nonlinearsuperposition of the rogue wave and breather solutions.