$A_n^{(1)}$ Toda Solitons: a Relation between Dressing transformations   and Vertex Operators
  Affine Toda equations based on simple Lie algebras arise by imposing zero curvature condition on a Lax connection which belongs to the corresponding loop Lie algebra in the principal gradation. In the particular case of $A_n^{(1)}$   Toda models, we exploit the symmetry of the underlying linear problem to calculate the dressing group element which generates arbitrary $N$-soliton solution from the vacuum. Starting from this result we recover the vertex operator representation of the soliton tau functions. 
H. Belich and R. Paunov