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We present a general approach to excite robust dissipative three-dimensionaland high-order solitons and breathers in passively driven nonlinear cavities.Our findings are illustrated in the paradigmatic example provided by an opticalKerr cavity with diffraction and anomalous dispersion, with the addition of anattractive three-dimensional parabolic potential. The potential breaks thetranslational symmetry along all directions, and impacts the system in aqualitatively unexpected manner: three-dimensional solitons, or light-bullets,are the only existing and stable states for a given set of parameters. Thisproperty is extremely rare, if not unknown, in passive nonlinear physicalsystems. As a result, the excitation of the cavity with any input field leadsto the deterministic formation of a target soliton or breather, with aspatiotemporal profile that unambiguously corresponds to the given cavity andpumping conditions. In addition, the tuning of the potential width along thetemporal direction results in the existence of a plethora of stable asymmetricsolitons. Our results may provide a solid route towards the observation ofdissipative light bullets and three-dimensional breathers.

Robust three-dimensional high-order solitons and breathers in driven dissipative systems: a Kerr cavity realization