  We describe the local structure of self-dual gradient Ricci solitons in
neutral signature. If the Ricci soliton is non-isotropic then it is locally
conformally flat and locally isometric to a warped product of the form
$I\times_\varphi N(c)$, where $N(c)$ is a space of constant curvature. If the
Ricci soliton is isotropic, then it is locally isometric to the cotangent
bundle of an affine surface equipped with the Riemannian extension of the
connection, and the Ricci soliton is described by the underlying affine
structure. This provides examples of self-dual gradient Ricci solitons which
are not locally conformally flat.
