Computation of partially invariant solutions for the Einstein Walker manifolds’ identifying equations

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 δ = 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.