  The nonlinear Schr\"odinger equation based on slowly varying approximation is
usually applied to describe the pulse propagation in nonlinear waveguides.
However, for the case of the front induced transitions (FITs), the pump effect
is well described by the dielectric constant perturbation in space and time.
Thus, a linear Schr\"odinger equation can be used. Also, in waveguides with
weak dispersion the spatial evolution of the pulse temporal profile is usually
tracked. Such a formulation becomes impossible for optical systems for which
the group index or higher dispersion terms diverge as is the case near the band
edge of photonic crystals. For the description of FITs in such systems a linear
Schr\"odinger equation can be used where temporal evolution of the pulse
spatial profile is tracked instead of tracking the spatial evolution. This
representation provides the same descriptive power and can easily deal with
zero group velocities. Furthermore, the Schr\"odinger equation with temporal
evolution can describe signal pulse reflection from both static and
counter-propagating fronts, in contrast to the Schr\"odinger equation with
spatial evolution which is bound to forward propagation. Here, we discuss the
two approaches and demonstrate the applicability of the spatial evolution for
the system close to the band edge where the group velocity vanishes by
simulating intraband indirect photonic transitions.
