Superregular breathers and state transitions in a resonant erbium-doped fiber system with higher-order effects

Highlights: • The dynamics of the superregular breather (SR) in an erbium doped fiber are investigated. • Such SR waves can exhibit unique half-transition and full-quasiannihilation states. • Different nonlinear waves can be evolved from an identical localized small perturbation. - Abstract: In this paper, we concentrate on the Hirota and Maxwell-Bloch (HMB) system governing the propagation of the femtosecond pulse in an erbium doped fiber. We present the superregular breather solutions that are nonlinear superposition of a pair of travelling breathers propagating in opposite directions. We further study the full- and half-transition modes of the superregular breather solution, which appears as a result of the coupled and higher-order effects. These waves reduce to small localized perturbations of the background at time zero.