  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.
