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 $\eta$, collisions between dark breathers and rogue waves are observed.

在本文中，我们旨在推导非线性Schrödinger和Maxwell-Bloch系统的退化孤子，呼吸和局部解，该系统受掺optical光纤中光脉冲的传播控制。基于以上获得的解决方案，观察到简并的暗孤子（呼吸），并分析了呼吸波和流浪之间的碰撞特征。尽管Darboux-dressing变换是导出本地化解的有效方法，但通过回顾和修改本手稿中的广义Darboux变换，我们相信找到了一种新颖的新方法来导出本地化解。详细地，用于复杂的现场包络$q$ 和极化 $p$，使用解决方案中的相应参数分析了明亮呼吸和流浪之间的碰撞。同时，对于人口倒置$\eta$，观察到黑暗呼吸者和流浪者之间发生了碰撞。