Stable dissipative soliton mMolecules in mode-locked laser

In this paper we show that stable soliton molecules can exist provided that one takes, the fast, however, noninstantaneous relaxation time of the saturable absorber into account. In order to double-check the result we used for both scenarios (non/instantaneous response) a more realistic lumped model for the fiber laser where each element (doped fiber with dispersive gain, saturable absorber and output coupler) has been modeled separately. Even in the lumped model the soliton molecules decayed for the instantaneous absorber, rather focus on the mode locked fiber laser as one specific system usually described by the CQGLE. We show, that the whole family of soliton molecules may be stabilized in this way.