  We report results of the investigation of gap solitons (GSs) in the generic
model of a periodically modulated Bragg grating (BG), which includes periodic
modulation of the BG chirp or local refractive index, and periodic variation of
the local reflectivity. We demonstrate that, while the previously studied
reflectivity modulation strongly destabilizes all solitons, the periodic chirp
modulation, which is a novel feature, stabilizes a new family of double-peak
fundamental BGs in the side bandgap at negative frequencies (gap No. -1), and
keeps solitons stable in the central bandgap (No. 0). The two soliton families
demonstrate bistability, coexisting at equal values of energy. In addition,
stable 4-peak bound states are formed by pairs of fundamental GSs in bandgap
-1. Self-trapping and mobility of the solitons are studied too.
