USING CONSERVATION-LAWS TO SOLVE TODA FIELD-THEORIES

We investigate the question of how the knowledge of sufficiently many local conservation laws for a model call be used to solve it. We show that for models where the conservation laws can be written in one-side d forms, like partial derivative Q(s) = 0, the problem can always be r educed to solving a closed system of ordinary differential equations. We investigate the A(1), A(2) and B-2 Toda field theor ies in consider able detail from this viewpoint. One of our findings is that there is in each case a transformation group intrinsic to the model. This group is built on a specific real form of the Lie algebra used to label the Toda field theory. It is the group of field transformations which lea ves the conserved densities invariant.