  Exact particle-like static, spherically and/or cylindrically symmetric
solutions to the equations of interacting scalar and electromagnetic field
system have been obtained. We considered Freedman-Robertson-Walker (FRW)
space-time as an external homogenous and isotropic gravitational field whereas
the homogeneous and anisotropic Universe is given by the G$\ddot o$del model.
Beside the usual solitonian solutions some special regular solutions know as
droplets, anti-droplets and bags (confined in finite interval and having
trivial value beyond it) have been obtained. It has been shown that in FRW
space-time equations with different interaction terms may have stable solutions
while within the scope of G$\ddot o$del model only the droplet-like and the
hat-like configurations may be stable, if they are located in the region where
$g^{00}>0$.
