  A certain non-Noetherian connection between symmetry and integrability
properties of nonlinear field equations in conservation-law form is studied. It
is shown that the symmetry condition alone may lead, in a rather
straightforward way, to the construction of a Lax pair, a doubly infinite set
of (generally nonlocal) conservation laws, and a recursion operator for
symmetries. Applications include the chiral field equation and the self-dual
Yang-Mills equation.
