Abstract
Dissipative localized structures, also known as cavity solitons, arise in the transverse plane of several nonlinear optical devices. We present two general mechanisms for their formation and some scenarios for their instability. In situations of coexistence of a homogeneous and a pattern state, we characterize excitable behavior mediated by localized structures. In this scenario, excitability emerges directly from the spatial dependence since it is absent in the purely temporal dynamics. In situations of coexistence of two homogeneous states, we discuss localized structures either due to the interaction of front tails (dark ring cavity solitons) or due to a balance between curvature effects and modulational instabilities of front solutions (stable droplets).
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