$A_n^{(1)}$ 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.

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

References in corpus (3)

• Tau-functions and Dressing Transformations for Zero-Curvature Affine Integrable Equations
• Seiberg-Witten theory, monopole spectral curves and affine Toda solitons
• Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories

Cited by in corpus (3)

• Tau-Functions generating the Conservation Laws for Generalized Integrable Hierarchies of KdV and Affine-Toda type
• SU(N) affine Toda solitons and breathers from transparent Dirac potentials
• Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations