Spatiotemporal surface Ginzburg-Landau solitons

We study spatiotemporal light localization in truncated one-dimensional arrays of optical waveguides in the presence of gain and loss. We demonstrate the existence of classes of continuous-discrete spatiotemporal Ginzburg-Landau solitons, which include the so-called dissipative surface light bullets localized near the edges of the truncated waveguide arrays. We find the domains of existence of such solitons in the relevant parameter space, for both on-site and intersite spatiotemporal dissipative solitons and for the states localized at the different distances from the surface. We show that the on-site solitons are stable in the whole domain of their existence, whereas all intersite solitons are unstable. We describe the complex instability-induced scenarios of the dynamics of dissipative surface solitons.