Abstract

Dissipative solitons are localized structures (LSs) found in a plethora of different fields of sciences, ranging from plant population ecology to nonlinear optics [1]. In the latter, temporal LSs have been extensively studied in dispersive Kerr cavities such as all-fiber resonators [2]. The formation of these LSs (and their type) is generally related to the coexistence of different states in two different bistable scenarios. The first scenario appears when a periodic state coexists with an uniform one, and consists in a portion of the first embedded in the second. These LSs undergo a bifurcation structure known as standard homoclinic snaking (SHS) [3]. In the second case, two uniform states coexist, and LSs consist in a plateau of one uniform state embedded in another one. These LSs undergo collapsed homoclinic snaking (CHS) [3]. One scenario which has not yet been investigated in nonlinear optics is the so-called tristable regime, where two uniform states coexist with one spatially periodic pattern [4]. This work focus on the impact of tristability on the formation of LSs in Kerr cavities. We show that tristability implies a smooth transition between the SHS and CHS scenarios. To induce tristability, higher order dispersion effects, such as fourth-order dispersion (FOD), must be considered.

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