Emergence of collapsed snaking related dark and bright Kerr dissipative solitons with quartic-quadratic dispersion

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.