Abstract :
In this work, by utilizing the nonlinear equations of motion of an incompressible, isotropic
thin elastic tube subjected to a variable initial stretches both in the axial and the radial
directions and the approximate equations of motion of an incompressible inviscid fluid,
which is assumed to be a model for blood, we have studied the propagation of nonlinear
waves in such a medium under the assumption of long wave approximation. Employing
the reductive perturbation method we obtained the variable coefficient forced KdV equation
as the evolution equation. By use of proper transformations for the dependent field
and independent coordinate variables, we have shown that this evolution equation reduces
to the conventional KdV equation, which admits the progressive wave solution. The
numerical results reveal that the wave speed is variable in the axial coordinate and it
decreases for increasing circumferential stretch (or radius). Such a result seems to be plausible
from physical considerations. We further observed that, the wave amplitude gets
smaller and smaller with increasing time parameter along the tube axis.
