INVERSE SCATTERING AND SOLITONS IN A(N-1) AFFINE TODA FIELD-THEORIES

We implement the inverse scattering method in the case of the A(n) aff ine Toda field theories, by studying the space-time evolution of simpl e poles in the underlying loop group. We find the known single-soliton solutions, as well as additional solutions with non-linear modes of o scillation 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 top ological charges as the standard solutions, so we do not shed any ligh t 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 in tegrated energy-momentum density can be calculated from the central ex tension of the loop group.