Moving discrete dissipative solitons in arrays of nonlinear cavities

We study nonlinear light dynamics in arrays of nonlinear cavities with cubic nonlinear response driven by an external inclined holding beam. We show analytically and numerically that both discreteness and inclination of the driving field can drastically change the conditions for modulational instability of light in dissipative systems. We find numerically the families of resting and moving discrete cavity solitons for arbitrary inclination of the driving field, both in discrete and continuous models. We analyze the crossover between stationary and moving cavity solitons and also study the novel collision features between these two types of dissipative solitons.