Soliton, Breather and Rogue Wave Solutions for the Nonlinear Schr?dinger Equation Coupled to a Multiple Self-Induced Transparency System

We derive an N-fold Darboux transformation for the nonlinear Schrödinger equation coupled to a multiple self-induced transparency system, which is applicable to optical fiber communications in the erbium-doped medium. The N-soliton, N-breather and Nth-order rogue wave solutions in the compact determinant representations are derived using the Darboux transformation and limit technique. Dynamics of such solutions from the first- to second-order ones are shown.