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arXiv · hep-th/9712249

Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations

H. Belich·G. Cuba·R. Paunov
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Abstract

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.

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H. Belich, G. Cuba, R. Paunov. 1997-12-29. Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations. https://doi.org/10.1063/1.532575

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