  Affine Toda theory is a relativistic integrable theory in two dimensions
possessing solutions describing a number of different species of solitons when
the coupling is chosen to be imaginary. These nevertheless carry real energy
and momentum. To each species of soliton there has to correspond an antisoliton
species. There are two different ways of realising the antisoliton whose
equivalence is shown to follow from a surprising identity satisfied within the
underlying affine Kac-Moody group. This is the classical analogue of the
crossing property of analytic S-matrix theory. Since a complex parameter
related to the coordinate of the soliton is inverted, this identity implies a
sort of modular transformation property of the soliton solution. The results
simplify calculations of explicit soliton solutions.
