Interactions of the solitons in periodic driven-dissipative systems supporting quasi-BIC states

The paper is devoted to the dynamics of dissipative gap solitons in the periodically corrugated optical waveguides whose spectrum of linear excitations contains a mode that can be referred to as a quasi-Bound State in the Continuum. These systems cansupport a large variety of stable bright and dark dissipative solitons that can interact with each other and with the inhomogeneities of the pump. One of the focus points of this work is the influence of slow variations of the pump on the behavior of the solitons. It is shown that for the fixed sets of parameters the effect of pump inhomogeneities on the solitons is not the same for the solitons of different kinds. The second main goal of the paper is systematic studies of the interaction between the solitons of the same or of different kinds. It is demonstrated that various scenarios of inter-soliton interactions can occur: the solitons can repulse each other or get attracted. In the latter case, the solitons can annihilate, fuse in a single soliton or form a new bound state depending on the kinds of the interacting solitons and on the system parameters.

Dissipative Josephson vortices in annular polariton fluids

We consider two concentric rings formed by bosonic condensates of exciton-polaritons. A circular superfluid flow of polaritons in one of the rings can be manipulated by acting upon the second annular polariton condensate. The complex coupling betweenthe rings with different topological charges triggers nucleation of stable Josephson vortices (JVs) which are revealed as topological defects of the angular dependence of the relative phase between rings. Being dependent on the coupling strength, the structure of the JV governs the difference of the mean angular momenta of the inner and the outer rings. At the vanishing coupling the condensates rotate independently demonstrating no correlations of their winding numbers. At the moderate coupling, the interaction between two condensates tends to equalize their mean angular momenta despite of the mismatch of the winding numbers demonstrating the phenomenology of a drag effect. Above the critical coupling strength the synchronous rotation is established via the phase slip events.