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A forced, variable coefficients Kor\-te\-weg-de Vries equation for amplitudesof long, nonlinear internal waves in a stratified shear flow over topography isderived when the magnitude of the basic flow is small. The derivation is doneby incorporating the basic flow in the perturbation series of the Taniuti andWei's reductive perturbation method. Istead of the long-wave Tailor-Goldsteinspectral problem, only the usual long-wave spectral problem for restedstratified media and a boundary value problem have to be solved for calculatingthe coefficients of obtained equation. Explicit expressions for thesecoefficients are presented.

An amplitude equation for long, nonlinear internal waves in a weak shear flow over topography