Temporal localized states in semiconductors: from spatially extended to delayed systems

The formation of optical localized states in semiconductor systems has been to date very much focussed on transverse dynamics. In this contribution, we build on some recent publications devoted to dissipative solitons in semiconductors in time domain to discuss the analogy between spatially extended and delayed dynamical systems. In particular, we study front dynamics and homoclinic connections in relation to localized states in delayed systems.