Modulation of non-linear waves in a viscous fluid contained in an elastic tube

In the present work, utilizing the non-linear equations of a prestressed thin elastic tube filled with an incompressible viscous fluid the propagation of weakly non-linear waves in such a medium is studied. Considering that the arteries are initially subjected to a large static transmural pressure P-0 and an axial stretch lambda (z) and, in the course of blood how, a finite-time-dependent displacement is added to this initial field, the non-linear equations governing the motion of the tube in the radial direction is obtained. Utilizing the reductive perturbation technique the amplitude modulation of weakly non-linear and dissipative but strongly dispersive waves is examined and the dissipative non-linear Schrodinger equation is obtained. Finally, the numerical solution of the evolution equation under the given initial condition is given and the stability condition of the solution is discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.