Different types of nonlinear localized and periodic waves in an erbium-doped fiber system

•Prolific nonlinear waves in an erbium-doped fiber system are demonstrated.•The wave dynamics is extracted from a unified exact solution.•The formation mechanism of multi-peak solitons is discussed.

We study nonlinear waves on a plane-wave background in an erbium-doped fiber system, which is governed by the coupled nonlinear Schrödinger and the Maxwell–Bloch equations. We find that prolific different types of nonlinear localized and periodic waves do exist in the system, including multi-peak soliton, periodic wave, antidark soliton, and W-shaped soliton (as well as the known bright soliton, breather, and rogue wave). In particular, the dynamics of these waves can be extracted from a unified exact solution, and the corresponding existence conditions are presented explicitly. Our results demonstrate the structural diversity of the nonlinear waves in this system.