  We theoretically investigate the dynamics, bifurcation structure and
stability of dark localized states emerging in Kerr cavities in the presence of
second- and fourth-order dispersion. These states form through the locking of
uniform wave fronts, or domain walls, connecting two coexisting stable uniform
states. They undergo a generic bifurcation structure known as collapsed
homoclinic snaking. We characterize the robustness of these states by computing
their stability and bifurcation structure as a function of the main control
parameter of the system. Furthermore, we show that by increasing the dispersion
of fourth order, bright localized states can be also stabilized.
