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

We investigate analytically and numerically the formation of temporal localized structures in all photonic crystal fiber resonator. These dissipative structures consist of isolated or randomly distributed peaks in an uniform background of the intensity profile. The number of peaks and their temporal distribution are determined solely by initial conditions. They exhibit multistability behavior in a finite range of parameters. A weakly nonlinear analysis is performed in the neighborhood of the first threshold associated with the modulational instability. We consider the regime where the instability is not degenerate. We show that the fourth order dispersion affects the threshold associated with the formation of bright temporal localized structures. We estimate analytically and numerically both the linear and the nonlinear correction to the velocity of moving temporal structures induced by a spontaneous broken reflection symmetry mediated by the third-order dispersion. Finally, we show that the third order dispersion affects the threshold associated with the moving temporal localized structures.