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

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

1996-12-03

arxiv.org/abs/hep-th/9612029v3

J.Math.Phys. 38 (1997) 4108-4127

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, Latex file, amssym.def needed, no figures; one new reference added

Scientific paper

10.1063/1.532086

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.

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