BJ is using two Marshall amps modified by Martin Golub in a Live setup combined with a CAE 3+SE preamp where they bypass the Marshalls Preamp sections for clean and mid sounds.
The Marshalls were used in the studio back in the days from what I have read. Now they use all sorts of amps, like modded Park, Hiwatt, Tweed Fender twin, Divided by 13 combo.
As for the profile created by Marko, I read here that it is an amp with the same "Dookie" mod that Green Day uses.
Sounds great as is but sounds better if you change the Cab and use one part of the Siggi Mehl Rigs.
There are plenty of rigs here that gets you close to their core sound (which changes depending on the period)
Recently I am experimenting with one of Gundy Keller rigs called Gundy Brain'sStrayDogs but have to cut back bass, mid and treble. That varies on the period I want to play but so far it sounds pretty close on a Gibson ES335 type guitar and it is pretty versatile.
Anyway, have fun!