  The non-linear sigma model of the dimensionally reduced Einstein (-Maxwell)
theory is diagonally embedded into that of the two-dimensional heterotic string
theory. Consequently, the embedded string backgrounds satisfy the
(electro-magnetic) Ernst equation. In the pure Einstein theory, the
Matzner-Misner SL(2,{\bf R}) transformation can be viewed as a change of
conformal structure of the compactified flat two-torus, and in particular its
integral subgroup SL(2,{\bf Z}) acts as the modular transformation. The Ehlers
SL(2,{\bf R}) and SL(2,{\bf Z}) similarly act on another torus whose conformal
structure is induced through the Kramer-Neugebauer involution. Either of the
Matzner-Misner and the Ehlers SL(2,{\bf Z}) can be embedded to a special
T-duality, and if the former is chosen, then the Ehlers SL(2,{\bf Z}) is shown
to act as the S-duality on the four-dimensional sector. As an application we
obtain some new colliding string wave solutions by using this embedding as well
as the inverse scattering method.
