Controlled merging and annihilation of localized dissipative structures in an AC-driven damped nonlinear Schr\"odinger system

We report studies of controlled interactions of localized dissipative structures in a system described by the AC-driven damped nonlinear Schr\"odinger equation. Extensive numerical simulations reveal a diversity of interaction scenarios that are governed by the properties of the system driver. In our experiments, performed with a nonlinear optical Kerr resonator, the phase profile of the driver is used to induce interactions 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.