  We investigate the question of how the knowledge of sufficiently many local
conservation laws for a model can be utilized to solve the model. We show that
for models where the conservation laws can be written in one-sided forms, like
$\barpartial Q_s = 0$, 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 theories 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.
