Non-linear waves in a viscous fluid contained in an elastic tube with variable cross-section

In the present work, treating the large arteries as a thin-walled, long and circularly cylindrical, prestressed elastic tube with variable cross-section and using the reductive perturbation method, we have studied the amplitude modulation of non-linear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, the evolution equation is obtained as the dissipative non-linear Schrödinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave 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.