$A_n^{(1)}$ Toda solitons and the dressing symmetry

Abstract

We present an elementary derivation of the soliton-like solutions in the $A_n^{(1)}$ Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are calculated. This enables us to obtain explicit expression for the element which by dressing group action, produces a generic soliton solution. In the particular example of monosolitons we suggest a relation to the vertex operator formalism, previously used by Olive, Turok and Underwood. Our results can also be considered as generalization of the approach to the sine-Gordon solitons, proposed by Babelon and Bernard.