  Carrier wave shocking is studied using the Pseudo-Spectral Spatial Domain
(PSSD) technique. We describe the shock detection diagnostics necessary for
this numerical study, and verify them against theoretical shocking predictions
for the dispersionless case. These predictions show Carrier Envelope Phase
(CEP) and pulse bandwidth sensitivity in the single-cycle regime. The flexible
dispersion management offered by PSSD enables us to independently control the
linear and nonlinear dispersion. Customized dispersion profiles allow us to
analyze the development of both carrier self-steepening and shocks. The results
exhibit a marked asymmetry between normal and anomalous dispersion, both in the
limits of the shocking regime and in the (near) shocked pulse waveforms.
Combining these insights, we offer some suggestions on how carrier shocking (or
at least extreme self-steepening) might be realised experimentally.
