Robust Three-Dimensional High-Order Solitons and Breathers in Driven Dissipative Systems: A Kerr Cavity Realization.

We present a general approach to excite robust dissipative three-dimensional and high-order solitons and breathers in passively driven nonlinear cavities. Our findings are illustrated in the paradigmatic example provided by an optical Kerr cavity with diffraction and anomalous dispersion, with the addition of an attractive three-dimensional parabolic potential. The potential breaks the translational symmetry along all directions, and impacts the system in a qualitatively unexpected manner: three-dimensional solitons, or light bullets, are the only existing and stable states for a given set of parameters.

Dissipative Kerr solitons, breathers, and chimera states in coherently driven passive cavities with parabolic potential.

We analyze the stability and dynamics of dissipative Kerr solitons (DKSs) in the presence of a parabolic potential. This potential stabilizes oscillatory and chaotic regimes, favoring the generation of static DKSs. Furthermore, the potential induces the emergence of new dissipative structures, such as asymmetric breathers and chimera-like states.