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-sided forms, like partial derivative Q(s) = 0, the problem can always be reduced to solving a closed system of ordinary differential equations. We investigate the A(1), A(2) and B-2 Toda field theor ies in considerable 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 leaves the conserved densities invariant.