Egb. Hohler et K. Olaussen, USING CONSERVATION-LAWS TO SOLVE TODA FIELD-THEORIES, International journal of modern physics A, 11(10), 1996, pp. 1831-1853
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.