Vertex Operator Representation of the Soliton Tau Functions in the Aₙ⁽¹⁾ Toda Models by Dressing Transformations

الأصل · EN

We study the relation between the group-algebraic approach and the dressing symmetry one to the soliton solutions of the Aₙ⁽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 Aₙ⁽ⁿ⁾ Toda models.