  We construct a hierarchy of pairwise commuting flows $d/dt_{i,n}$ indexed by
$i \in \{1,2 \}$ and $n \in \mathbb{Z}_{\geq 0}$ on triples $(\mathcal{L}_1,
\mathcal{L}_2, \mathcal{H})$ where $\partial_1$ and $\partial_2$ are two
commuting derivations, $\partial_i \mathcal{L}_i$ is a self-adjoint
pseudodifferential operator in $\partial_i$ and $\mathcal{H}$ is the formal
Schr\"{o}dinger operator $\mathcal{H}=\partial_1 \partial_2 +u$.
$\mathcal{L}_1, \mathcal{L}_2$ and $\mathcal{H}$ are coupled by the relations
$\mathcal{H} \mathcal{L}_i+\mathcal{L}_i^* \mathcal{H}=0$. We show that the
flows $d/dt_{1,n}+d/dt_{2,n}$ commute with the involution $(\mathcal{L}_1,
\mathcal{L}_2, \mathcal{H}) \mapsto (\mathcal{L}_2, \mathcal{L}_1,
\mathcal{H})$ and that the first equation of this reduced hierarchy is the
Novikov-Veselov equation.
