Complexes and molecules of dissipative solitons in mode-locked lasers

The concept of a dissipative soliton has become an important tool for the exploration and the analysis of the multiple pulse dynamics, with mode-locked lasers and regenerated transmission lines as important applications. Above all, the study of dissipative solitons has become a fertile area of nonlinear science with multidisciplinary implications. The aim of this talk is to present recent developments of dissipative soliton interactions in two marked different situations. Several years ago, robust soliton pairs were predicted from the cubic-quintic Ginzburg-Landau equation (CGLE) and subsequently observed in mode-locked fiber lasers. Recently, it was shown that soliton pairs in fiber lasers could have stable vibrational motions too, explained as attractors of limit-cycle type. The analogy between with matter molecules and soliton complexes or "molecules", although limited in validity, appears as a fruitful ground for investigation.