  We generalize the concept of nonlinear periodic structures to systems that
show arbitrary spacetime variations of the refractive index. Nonlinear pulse
propagation through these spatiotemporal photonic crystals can be described,
for shallow nonstationary gratings, by coupled mode equations which are a
generalization of the traditional equations used for stationary photonic
crystals. Novel gap soliton solutions are found by solving a modified massive
Thirring model. They represent the missing link between the gap solitons in
static photonic crystals and resonance solitons found in dynamic gratings.
