Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories

Abstract

We implement the inverse scattering method in the case of the $A_n$ affine Toda field theories, by studying the space-time evolution of simple poles in the underlying loop group. We find the known single soliton solutions, as well as additional solutions with non-linear modes of oscillation around the standard solution, by studying the particularly simple case where the residue at the pole is a rank one projection. We show that these solutions with extra modes have the same mass and topological charges as the standard solutions, so we do not shed any light on the missing topological charge problem in these models. We also show that the integrated energy-momentum density can be calculated from the central extension of the loop group.

28 pages, Latex, 4 figs included

References in corpus (2)

• Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories
• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories

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• Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories
• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories
• Abelian Toda solitons revisited
• Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories II
• $A_n^{(1)}$ Toda solitons and the dressing symmetry
• Inverse scattering and the symplectic form for sine-Gordon solitons
• Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations
• The braiding for representations of q-deformed affine $s{l}_2$