  In recent years it has been shown that many, and possibly all, integrable
systems can be obtained by dimensional reduction of self-dual Yang-Mills. I
show how the integrable systems obtained this way naturally inherit
bihamiltonian structure. I also present a simple, gauge-invariant formulation
of the self-dual Yang-Mills hierarchy proposed by several authors, and I
discuss the notion of gauge equivalence of integrable systems that arises from
the gauge invariance of the self-duality equations (and their hierarchy); this
notion of gauge equivalence may well be large enough to unify the many diverse
existing notions.
