Steady states of dissipative optical solitons in erbium-doped single-mode fiber amplifiers

The steady states for ultrashort dissipative optical solitons, appearing in single-mode erbium-doped fiber amplifiers are theoretically examined. Such solitons can be shaped due to resculpturing external optical pulses by fiber amplifier in the traveling-wave regime. We consider rather simplified model related to the most desirable practically fundamental solitons and, in so doing, develop extremely extended analytical approach based on exploiting the consistency equation. The analysis performed includes the already-known data for the model selected, generalizes them, and demonstrates that erbium doped fiber amplifiers can support both dark and bright dissipative optical solitons as well as the shock waves, whose amplitude and frequency profiles are exactly described.