  Static, cylindrically symmetric solutions to nonlinear scalar-Einstein
equations are considered. Regularity conditions on the symmetry axis and flat
or string asymptotic conditions are formulated in order to select soliton-like
solutions. Some non-existence theorems are proved, in particular, theorems
asserting (i) the absence of black-hole and wormhole-like cylindrically
symmetric solutions for any static scalar fields minimally coupled to gravity
and (ii) the absence of solutions with a regular axis for scalar fields with
the Lagrangian $L=F(I)$, $I=\phi^\alpha \phi_\alpha$, for any function $F(I)$
possessing a correct weak field limit. Exact solutions for scalar fields with
an arbitrary potential function $V(\phi)$ are obtained by quadratures and are
expressed in a parametric form in a few ways, where the parameter may be either
the coordinate $x$, or the $\phi$ field, or one of the metric coefficients.
Soliton-like solutions are shown to exist only with $V(\phi)$ having a variable
sign. Some explicit examples of solutions (including a soliton-like one) and
their flat-space limit are discussed.}
