Two-dimensional solitons and clusters in dissipative lattices

We study the dynamics of two-dimensional spatial solitons in the structured optical medium modeled by the complex Ginzburg-Landau equation with cubic-quintic nonlinearity and a spatially periodic modulation of the local gain-loss coefficient [a dissipative lattice (DL)]. The analysis, following the variation of the DL's amplitude and period, reveals several dynamical scenarios: stable or unstable propagation of a single dissipative soliton (the unstable propagation entails generation of an irregular multisoliton cluster), transformation of the input soliton into stable or unstable regular clusters patterned as the underlying DL, and decay of the input. Most results are obtained by means of systematic simulations, but the boundary of the single-soliton stability domain is explained analytically.