Analytical description of the multi-wave effects in the dynamical diffraction theory

An approximate analytical solution of the dispersion equation of the multi-wave dynamical X-ray diffraction theory is found with the accuracy of second order by X-ray susceptibility of a crystal. The expressions are obtained in covariant form, which is not connected with the definite Bragg peak, and allows one to analyze the long-range scans in the high-resolution X-ray diffractometry. (authors)