  In this paper, partially invariant solutions (PISs) method is applied in
order to obtain new four-dimensional Einstein Walker manifolds. This method is
based on subgroup classification for the symmetry group of partial differential
equations (PDEs) and can be regarded as the generalization of the similarity
reduction method. For this purpose, those cases of PISs which have the defect
structure delta=1 and are resulted from two-dimensional subalgebras are
considered in the present paper. Also it is shown that the obtained PISs are
distinct from the invariant solutions that obtained by similarity reduction
method.
