Nonlinear wave modulation in a fluid-filled linearly tapered elastic tube

In the present work, treating the arteries as a thin-walled, linearly tapered, prestressed elastic tube and using the reductive perturbation method, we have studied the amplitude modulation of nonlinear 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 nonlinear Schrödinger equation with variable coefficient. It is shown that this type of evolution equations admit a solitary wave type of solution with variable wave speeds and amplitude. It is observed that, the speed of enveloping wave increases with the scaled time parameter τ for negative tapering angle while it decreases for positive tapering. On the other hand, the speed of harmonic wave increases for positive tapering whereas it decreases for negative tapering.