  We study the relation between the group-algebraic approach and the dressing
symmetry one to the soliton solutions of the $A_n^{(1)}$ Toda field theory in
1+1 dimensions. Originally solitons in the affine Toda models has been found by
Olive, Turok and Underwood. Single solitons are created by exponentials of
elements which ad-diagonalize the principal Heisenberg subalgebra.
Alternatively Babelon and Bernard exploited the dressing symmetry to reproduce
the known expressions for the fundamental tau functions in the sine-Gordon
model. In this paper we show the equivalence between these two methods to
construct solitons in the $A_n^{(n)}$ Toda models.
