A (1) n Toda Solitons: a Relation between Dressing transformations and Vertex Operators
Abstract
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
(1)
n
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.