  A forced, variable coefficients Kor\-te\-weg-de Vries equation for amplitudes
of long, nonlinear internal waves in a stratified shear flow over topography is
derived when the magnitude of the basic flow is small. The derivation is done
by incorporating the basic flow in the perturbation series of the Taniuti and
Wei's reductive perturbation method. Istead of the long-wave Tailor-Goldstein
spectral problem, only the usual long-wave spectral problem for rested
stratified media and a boundary value problem have to be solved for calculating
the coefficients of obtained equation. Explicit expressions for these
coefficients are presented.
