Stable Soliton Excitations in Modulational Instability Regime with the Fourth-order Effects

We study the correspondence between modulational instability and types of fundamental nonlinear excitation in a nonlinear fiber with both third-order and fourth-order effects. Some stable soliton excitations are obtained in modulational instability regime, which have not been found in nonlinear fibers with second-order effects and third-order effects. Explicit analysis suggests that the stable soliton existence is related with the modulation stability circle in the modulation instability regime, and they just exist in the modulational instability regime outside of the modulational stability circle. It should be emphasized that the stable soliton just exist with two special profiles on a continuous wave background with certain frequency. The evolution stability of the solitons is tested numerically, which indicate they are robust against perturbations even in modulation instability regime. The further analysis indicates that the solitons in modulational instability regime are caused by the fourth-order effects.