Forced perturbed Korteweg-de Vries equation in an elastic tube filled with a viscous fluid

In the present work, treating the arteries as a prestressed thin walled elastic tube with a stenosis and the blood as a Newtonian fluid, we have studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method [A. Jeffrey, T. Kawahara, Asymptotic Methods in Nonlinear Wave Theory, Pitman, Boston, 1981]. We obtained the forced perturbed Korteweg-de Vries equation with variable coefficients as the evolution equation. By use of the coordinate transformation, it is shown that this type of evolution equation admits a progressive wave solution with variable wave speed. As might be expected from physical consideration, the wave speed reaches its maximum value at the center of stenosis and gets smaller and smaller as we go away from the center of the stenosis. The results seem to be consistent with physical intuitions.