  It is shown that electro (magneto) static sector of Maxwell's electrodynamics
coupled to the dilaton field in a string theory form possesses the symmetry
group of the stationary General Relativity in vacuum. Performing the Ernst
formalism, we develope a technique for generation of exact solutions in this
modified electrodynamics on the base of the normalized Ehlers symmetry
transformation. In the electrostatic case, we construct and study a general
class of spherically symmetric solutions that describes a point-like sourse of
the Coulomb type. It is shown that this source is characterized by asymptotical
freedom of the electrostatic interaction at short distances. Also it is
established that the total electrostatic energy of this source is finite and
inversely proportional to the dilaton-Maxwell coupling constant.
