  In this paper we report on a local classification of four dimensional Ricci
solitons which have a $2$-dimensional Abelian Killing algebra
$\mathcal{G}_{2}$, whose Killing leaves are non-null and orthogonally
intransitive. The classification is obtained under the following additional
assumptions: (i) the curvature vector field, of the submersion defined by
$\mathcal{G}_{2}$, is a null vector field; (ii) $\mathcal{G}_{2}$ has a null
vector; (iii) the vector field of the Ricci soliton is tangent to the Killing
leaves and a symmetry of the orthogonal distribution. Since there are only few
examples of orthogonally intransitive Einstein metrics, and even less is known
about orthogonally intransitive Ricci solitons, we believe that these results
can help fill this gap in the literature.
