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Yayın Amplitude modulation of nonlinear waves in a fluid-filled tapered elastic tube(Wiley-V C H Verlag, 2003) Demiray, HilmiIn the present work, treating the arteries as a tapered, thin walled, long, and circularly conical prestressed elastic tube and using the reductive perturbation method, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible non-viscous fluid, the evolution equation is obtained as the nonlinear Schrodinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave type of solution with a variable wave speed. It is observed that the wave speed increases with distance for narrowing tubes while it decreases for expanding tubes.Yayın Waves in fluid-filled elastic tubes with a stenosis: Variable coefficients KdV equations(Elsevier B.V., 2007-05-15) Demiray, HilmiIn the present work, by treating the arteries as thin-walled prestressed elastic tubes with a stenosis and the blood as an inviscid fluid we have studied the propagation of weakly nonlinear waves in such a medium, in the longwave approximation, by employing the reductive perturbation method. The variable coefficients KdV and modified KdV equations are obtained depending on the balance between the nonlinearity and the dispersion. By seeking a localized progressive wave type of solution to these evolution equations, we observed that the wave speeds takes their maximum values at the center of stenosis and gets smaller and smaller as one goes away from the stenosis. Such a result seems to reasonable from the physical point of view.
