Degenerate soliton, breather and localized solutions for a nonlinear Schrödinger and Maxwell–Bloch system

Abstract

In this paper, we aim to derive the degenerate soliton, breather and localized solutions for a nonlinear Schrödinger and Maxwell–Bloch system, which is governed by optical pulse propagation in an erbium-doped fiber. Based on the above solutions obtained, the degenerate bright and dark solitons (breathers) are observed and collision features between breathers and rogue waves are analyzed. Though Darboux-dressing transformation is an efficient method for deriving the localized solutions, by recalling and modifying the generalized Darboux transformation in this manuscript, we trust to find a novel and new way to derive the localized solutions. In detail, for complex field envelope q and polarization p, collisions between bright breathers and rogue waves are analyzed with corresponding parameters in the solutions. Meanwhile, for population inversion η, collisions between dark breathers and rogue waves are observed.