  We found the self-similar solitary solutions of a recently proposed model for
propagation of pulses in gas filled hollow-core photonic crystal fibers that
includes a plasma induced nonlinearity. As anticipated for a simpler model and
using a perturbation analysis, there are indeed stationary solitary waves that
accelerate and self-shift to higher frequencies. However, if the plasma
nonlinearity strength is large or the pulse amplitudes are small, the solutions
have distinguished long tails and decay as they propagate.
