  We present a connection between the Killing fields that arise in the
loop-group approach to integrable systems and conservation laws viewed as
elements of the characteristic cohomology. We use the connection to generate
the complete set of conservation laws (as elements of the characteristic
cohomology) for the Tzitzeica equation, completing the work in Fox and
Goertsches (2011).
  We define a notion of finite-type for integral manifolds of exterior
differential systems directly in terms of conservation laws that generalizes
the definition of Pinkall-Sterling (1989). The definition applies to any
exterior differential system that has infinitely many conservation laws
possessing a normal form.
  Finally, we show that, for the rank-one Toda field equations, every
characteristic cohomology class has a translation invariant representative as
an undifferentiated conservation law. Therefore the characteristic cohomology
defines de Rham cohomology classes on doubly periodic solutions.
