  The cross section for scattering of x-rays by solitons is calculated. The
authors consider solitons corresponding to the formation of a kink in a system
of adatoms on the surface of a substrate, or of a crowdion in a chain of atoms
in a crystal that are described by the sine-Gordon equation. It is shown that
investigation of the x-ray scattering makes it possible to obtain information
about the static and dynamic properties of the solitons.
