Inverse scattering and solitons in An−1 affine Toda field theories Original Research Article

We implement the inverse scattering method in the case of the An 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. From the monodromy matrix it is shown that these solutions have the same higher conserved charges as the standard solutions. We also show that the integrated energy-momentum density can be calculated from the central extension of the loop group.