  Frequency blueshifting was recently observed in light pulses propagating on
gas filled hollow-core photonic crystal fibers where a plasma has been produced
due to photoionization of the gas. One of the propagation models that is
adequate to describe the actual experimental observations is here investigated.
It is a nonlinear Schr\"odinger equation with an extra term, to which we
applied a self-similar change of variables and found its accelerating solitons.
As in other NLS related models possessing accelerating solitons, there exist
asymmetrical pulses that decay as they propagate in some parameter region that
was here well defined.
