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