  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.
