Exact S-matrices for d(n+1)((2)) affine Toda solitons and their bound states

We conjecture an exact S-matrix for the scattering of solitons in d(n+1)((2)), affine Toda field theory in terms of the R-matrix of the quantum group U-q(c(n)((1))). From this we construct the scattering amplitudes for all scalar bound states (breathers) of the theory. This S-matrix conjecture is justified by detailed examination of its pole structure. We show that a breather-particle identification holds by comparing the S-matrix elements for the lowest breathers with the S-matrix for the quantum particles in real affine Toda field theory, and discuss the implications for various forms of duality.