  We analyze the stability and dynamics of dissipative Kerr solitons 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. Based on a mode decomposition of
these states, we unveil the underlying modal interactions.
