N -order bright and dark rogue waves in a resonant erbium-doped fiber system

The rogue waves in a resonant erbium-doped fiber system governed by a coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the breather solutions of the normalized slowly varying amplitude of the complex field envelope E, polarization p, and population inversion η. The n-order breather solutions of the three fields are constructed using a Darboux transformation (DT) by assuming periodic seed solutions. Moreover, the n-order rogue waves are given by determinant forms with n+3 free parameters. Furthermore, the possible connection between our rouge waves and the generation of supercontinuum generation is discussed.