Non-linear waves in a fluid-filled inhomogeneous elastic tube with variable radius

In the present work, by employing the non-linear equations of motion of an incompressible, inhomogeneous, isotropic and prestressed thin elastic tube with variable radius and the approximate equations of an inviscid fluid, which is assumed to be a model for blood, we studied the propagation of non-linear waves in such a medium, in the longwave approximation. Utilizing the reductive perturbation method we obtained the variable coefficient Korteweg–de Vries (KdV) equation as the evolution equation. By seeking a progressive wave type of solution to this evolution equation, we observed that the wave speed decreases for increasing radius and shear modulus, while it increases for decreasing inner radius and the shear modulus.