Abstract

Modulation of Nonlinear Waves in a Fluid-Filled Tapered Elastic Tube

H.Demiray (Department of Mathematics, Faculty of Arts and Sciences, Isik University, Maslak Istanbul, Turkey)

e-mail: demiray@isikun.edu.tr

In the present work, treating the arteries as a tapered, thin walled, prestressed long and circularly conical tube and blood as an inviscid fluid, the modulation of nonlinear waves in such a medium is studied. For that purpose, the nonlinear dynamical equations of motion of a prestressed conical tube filled with an incompressible fluid are obtained. Assuming that the tapering angle is of order e^4, where e is a small parameter measuring the weakness of nonlinearity, and utilizing the reductive perturbation technique, the modulation of nonlinear waves is studied and the nonlinear Schrцdinger equation with variable coefficients is obtained as the governing evolution equation. A solitary wave type of solution to this nonlinear equation with variable coefficient is obtained. It is observed that, in contrast to the solitary waves in tubes with constant radius, in tapered tubes the speed of the wave is variable; that is, the wave speed increases with distance for descending tubes, whereas it decreases with distance for ascending tubes.

Section : 5