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 positive second-and fourth-order dispersion. In this previously unexplored regime, dark states form through the locking of uniform wave fronts, or domain walls, connecting two coexisting stable uniform states, and 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.

Automated summary

In this paper, we theoretically investigate the dynamics, bifurcation structure, and stability of dark localized states in Kerr cavities with positive second- and fourth-order dispersion. We found that dark states form through the locking of uniform wave fronts, or domain walls, and undergo a bifurcation structure known as collapsed homoclinic snaking. We also showed that increasing the dispersion of fourth order can stabilize bright localized states.