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

We report studies of controlled interactions of localised dissipative structures in a system described by the AC-driven damped nonlinear Schrodinger 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 fibre (Kerr) resonator, the phase profile of the driver is used to induce interactions of the dissipative structures on demand. We observe both merging and annihilation of localised structures, i.e. interactions governed by the dissipative, out-of-equilibrium nature of the system. These interactions fundamentally differ from those typically found for conventional conservative solitons.