Solitons with adjustable relative phase on plane-wave backgrounds in erbium-doped fiber systems

We investigate the impact of relative phase on the excitation characteristics of Kuznetsov-Ma breathers and solitons on a plane-wave background within an erbium-doped optical fiber system, described by the nonlinear Schrödinger Maxwell-Bloch equation. We derive the Kuznetsov-Ma breather and soliton solutions with adjustable relative phases and identify the parameter ranges for different types of these nonlinear waves. We find that the relative phase can significantly alter the distribution of solitons and even change their types, thereby enabling a diverse array of soliton structures through phase adjustments. The relative phase does not alter the overall structure of Kuznetsov-Ma breathers, as it varies with the propagation distance. Notably, solitons with different relative phases and Kuznetsov-Ma breathers at corresponding positions along their evolution share identical distribution patterns. This consistency underscores the intrinsic relationship between unstable nonlinear waves and their stable counterparts across various nonlinear systems. These findings enhance our understanding of the role of relative phase in nonlinear wave dynamics and provide important insights into the control and manipulation of nonlinear wave structures.