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

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

1996-10-15

arxiv.org/abs/hep-th/9610104v2

Nucl.Phys. B484 (1997) 653-681

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, Latex, 4 figs included

Scientific paper

10.1016/S0550-3213(96)00576-7

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.

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