Equations for the self-consistent field in random medium

An integral-differential equation is derived for the self-consistent (effective) field in the medium consisting of many small bodies randomly distributed in some region. Acoustic and electromagnetic fields are considered in such a medium. Each body has a characteristic dimension a<<λ, where λ is the wavelength in the free space. The minimal distance d between any of the two bodies satisfies the condition d>>a, but it may also satisfy the condition d<<λ in acoustic scattering. In electromagnetic scattering our assumptions are a<<λ and λ<<d. Using Ramm's theory of wave scattering by small bodies of arbitrary shapes, the author derives an integral-differential equation for the self-consistent acoustic or electromagnetic fields in the above medium