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We report studies of controlled interactions of localized dissipative structures in a system described by the AC-driven damped nonlinear Schrödinger equation (equivalent to the Lugiato-Lefever model). Extensive numerical simulations reveal a variety of interaction scenarios that are governed by the properties of the system driver, notably its gradients. In our experiments, performed with a nonlinear optical bre (Kerr) resonator, the phase prole of the driver is used to induce interactions of the dissipative structures on demand. We observe both merging and annihilation of localized structures, i.e. interactions governed by the dissipative, out of-equilibrium nature of the system. These interactions fundamentally dier from those typically found for conventional conservative solitons

Controlled merging and annihilation of localised dissipative structures in an AC-driven damped nonlinear Schrödinger system