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