  We present in detail our developed model [Saleh et al., Phys. Rev. Lett. 107]
that governs pulse propagation in hollow-core photonic crystal fibers filled by
an ionizing gas. By using perturbative methods, we find that the
photoionization process induces the opposite phenomenon of the well-known Raman
self-frequency red-shift of solitons in solid-core glass fibers, as was
recently experimentally demonstrated [Hoelzer et al., Phys. Rev. Lett. 107].
This process is only limited by ionization losses, and leads to a constant
acceleration of solitons in the time domain with a continuous blue-shift in the
frequency domain. By applying the Gagnon-B\'{e}langer gauge transformation,
multi-peak `inverted gravity-like' solitary waves are predicted. We also
demonstrate that the pulse dynamics shows the ejection of solitons during
propagation in such fibers, analogous to what happens in conventional
solid-core fibers. Moreover, unconventional long-range non-local interactions
between temporally distant solitons, unique of gas plasma systems, are
predicted and studied. Finally, the effects of higher-order dispersion
coefficients and the shock operator on the pulse dynamics are investigated,
showing that the resonant radiation in the UV [Joly et al., Phys. Rev. Lett.
106] can be improved via plasma formation.
