  In this paper the well known Belinskii and Zakharov soliton generating
transformations of the solution space of vacuum Einstein equations with
two-dimensional Abelian groups of isometries are considered in the context of
the so called "monodromy transform approach", which provides some general base
for the study of various integrable space - time symmetry reductions of
Einstein equations. Similarly to the scattering data used in the known spectral
transform, in this approach the monodromy data for solution of associated
linear system characterize completely any solution of the reduced Einstein
equations, and many physical and geometrical properties of the solutions can be
expressed directly in terms of the analytical structure on the spectral plane
of the corresponding monodromy data functions. The Belinskii and Zakharov
vacuum soliton generating transformations can be expressed in explicit form
(without specification of the background solution) as simple
(linear-fractional) transformations of the corresponding monodromy data
functions with coefficients, polynomial in spectral parameter. This allows to
determine many physical parameters of the generating soliton solutions without
(or before) calculation of all components of the solutions. The similar
characterization for electrovacuum soliton generating transformations is also
presented.
