Callahan Fullbore Autolock
The Callahan full-bore autolock is the make and model of Jayne's BFG. It featured a customized hair-trigger and double-cartridge thorough gauge. Though it's not obvious, this would seem to indicate that the weapon can dynamically switch bore sizes depending on the size of cartridge the user desires. This weapon is introduced when Jayne tries to trade his "Vera" to Mal in exchange for Saffron in Our Mrs Reynolds.
It is worth noting that the Callahan is the only weapon on Serenity (or at least in Jayne's collection) that has armor-piecing capabilities: though Jayne is unsure whether it would be able to pierce the hull of Serenity herself.
"Vera" also appeared in the movie "Showtime" with Eddie Murphy and Robert De Niro, and she is modeled with (mostly) bolt-on parts on top of a Russian "Saiga-12" Kalishnikov-style shotgun.