  We present a numerical investigation of the propagation dynamics of a
truncated Airy pulse in a highly dispersive and nonlinear medium by employing
the split-step Fourier transform method and look, in particular, into the
effects of fourth order dispersion (FOD) and cubic-quintic-septic nonlinearity
on pulse evolution. Presence of FOD cancels the Airy pulse self-acceleration
along with eclipsing the oscillatory tail during propagation in the linear
regime. Further, we observe soliton shedding at low input pulse power in the
presence of cubic and quintic nonlinearity and negative FOD. The emergent
soliton exhibits temporal shift and the direction and the extent of the shift
depend upon the strengths of cubic and quintic nonlinearities. In the presence
of anomalous group velocity dispersion (GVD) with negative FOD, soliton
shedding is observed at relatively high input pulse power. The strengths of GVD
and nonlinearity play a vital role in the temporal shifting of emergent
soliton. Furthermore, we have explored the effects of septic nonlinearity on
soliton shedding in different scenarios of nonlinearity and dispersion.
