Article ID Journal Published Year Pages File Type
758411 Communications in Nonlinear Science and Numerical Simulation 2013 8 Pages PDF
Abstract

•Some new classes of 4-dim Einstein Walker manifolds are constructed by partially invariant solutions method.•An optimal system of invariant solutions of this class of equations is obtained.•The non-reducible partially invariant solutions are obtained.•Some new examples of four-dimensional Einstein Walker manifolds are obtained by this method.

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=1δ=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.

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Physical Sciences and Engineering Engineering Mechanical Engineering
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