AFFINE SOLITONS - A RELATION BETWEEN TAU-FUNCTIONS, DRESSING AND BACKLUND-TRANSFORMATIONS

We reconsider the construction of solitons by dressing transformations in the sine-Gordon model. We show that the N-soliton solutions are in the orbit of the vacuum, and we identify the elements in the dressing group which allow us to build the N-soliton solutions from the vacuum solution. The dressed tau functions can be computed in two different ways: either using adjoint actions in the affine Lie algebra sl2, and this gives the relation with the Backlund transformations, or using the level-one representations of the affine Lie algebra sl2, and this directly gives the formulae for the tau fuctions in terms of vertex operators.