  We provide new expressions for the scattering amplitudes in the
soliton-antisoliton sector of the elliptic sine-Gordon model in terms of cosets
of the affine Weyl group corresponding to infinite products of q-deformed gamma
functions. When relaxing the usual restriction on the coupling constants, the
model contains additional bound states which admit an interpretation as
breathers. These breather bound states are unavoidably accompanied by Tachyons.
We compute the complete S-matrix describing the scattering of the breathers
amonst themselves and with the soliton-antisoliton sector. We carry out various
reductions of the model, one of them leading to a new type of theory, namely an
elliptic version of the minimal D(n+1)-affine Toda field theory.
