Solution
= Solution
Let $D_\mu=\partial_\mu+A_\mu$. A <Lax pair> with spectral parameter $\lambda$ is
$$
\boxed{L(\lambda)=D_w-\lambda D_{\bar z},
\qquad
M(\lambda)=D_z+\lambda D_{\bar w}}.
$$
The coefficients of $[L,M]=0$ at orders $1,\lambda,\lambda^2$ are respectively
$$
F_{wz}=0,\qquad F_{w\bar w}+F_{z\bar z}=0,\qquad F_{\bar w\bar z}=0,
$$
which are precisely the anti-self-dual Yang-Mills equations.