  The question of complete integrability of evolution equations associated to
$n\times n$ first order isospectral operators is investigated using the inverse
scattering method. It is shown that for $n>2$, e.g. for the three-wave
interaction, additional (nonlinear) pointwise flows are necessary for the
assertion of complete integrability. Their existence is demonstrated by
constructing action-angle variables. This construction depends on the analysis
of a natural 2-form and symplectic foliation for the groups GL(n) and SU(n).}
