Bright and dark solitons in pure quartic Kerr resonators

The excitation of temporal cavity solitons in fiber and microring resonators has important implications into nonlinear science and technology such as the generation of frequency combs. Temporal solitons are robust against strong perturbations coming from the so-called higher order effects. Particularly interesting are those coming from higher order chromatic dispersion, which have been shown to impact positively in soliton formation and in their stability. In this work we unveil the bifurcation structure and stability of bright and dark Kerr solitons in the presence of pure fourth order dispersion (FOD), in the normal and anomalous group velocity dispersion (GVD) regime. Under a dominant FOD, the time evolution of the intracavity field envelop, A, may be described by the pure quartic Lugiato-Lefever equation.