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We investigate analytically and numerically the formation of temporallocalized structures in all photonic crystal fiber resonator. These dissipativestructures consist of isolated or randomly distributed peaks in an uniformbackground of the intensity profile. The number of peaks and their temporaldistribution are determined solely by initial conditions. They exhibitmultistability behavior in a finite range of parameters. A weakly nonlinearanalysis is performed in the neighborhood of the first threshold associatedwith the modulational instability. We consider the regime where the instabilityis not degenerate. We show that the fourth order dispersion affects thethreshold associated with the formation of bright temporal localizedstructures. We estimate analytically and numerically both the linear and thenonlinear correction to the velocity of moving temporal structures induced by aspontaneous broken reflection symmetry mediated by the third-order dispersion.Finally, we show that the third order dispersion affects the thresholdassociated with the moving temporal localized structures.

Temporal localized structures in photonic crystal fiber resonators and their spontaneous symmetry breaking instability