  An accurate and efficient simulation has been devised, employing a new
numerical technique to simulate the derivative generalised non-linear
Schr\"odinger equation in all three spatial dimensions and time. The simulation
models all pertinent effects such as self-steepening and plasma for the
non-linear propagation of ultrafast optical radiation in bulk material.
Simulation results are compared to published experimental spectral data of an
example ytterbium aluminum garnet system at 3.1um radiation and fits to within
a factor of 5. The simulation shows that there is a stability point near the
end of the 2 mm crystal where a quasi-light bullet (spatial temporal soliton)
is present. Within this region, the pulse is collimated at a reduced diameter
(factor of ~2) and there exists a near temporal soliton at the spatial center.
The temporal intensity within this stable region is compressed by a factor of
~4 compared to the input. This study shows that the simulation highlights new
physical phenomena based on the interplay of various linear, non-linear and
plasma effects that go beyond the experiment and is thus integral to achieving
accurate designs of white light generation systems for optical applications. An
adaptive error reduction algorithm tailor made for this simulation will also be
presented in appendix.
