Rogue waves in a resonant erbium-doped fiber system with higher-order effects
arXiv:1505.02237 · doi:10.1016/j.amc.2015.10.015
Abstract
We mainly investigate a coupled system of the generalized nonlinear Schrödinger equation and the Maxwell-Bloch equations which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order effects including the forth-order dispersion and quintic non-Kerr nonlinearity. We derive the one-fold Darbox transformation of this system and construct the determinant representation of the $n$-fold Darboux transformation. Then the determinant representation of the $n$th new solutions $(E^{[n]},\, p^{[n]},\, η^{[n]})$ which were generated from the known seed solutions $(E, \, p, \, η)$ is established through the $n$-fold Darboux transformation. The solutions $(E^{[n]},\, p^{[n]},\, η^{[n]})$ provide the bright and dark breather solutions of this system. Furthermore, we construct the determinant representation of the $n$th-order bright and dark rogue waves by Taylor expansions and also discuss the hybrid solutions which are the nonlinear superposition of the rogue wave and breather solutions.
25 Pages Applied Mathematics and Computation 273(2016) 826-841