Treating arteries as thin-walled prestressed elastic tubes with a narrowing (stenosis) and blood as an inviscid fluid we study the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method in the long wave approximation. It is shown that the evolution equation of the first-order term in the perturbation expansion may be described by the conventional Korteweg-de Vries (KdV) equation. The evolution equation for the second-order term is ...