Solitary waves in elastic tubes filled with a layered fluid

Abstract

In this work, we studied the propagation of weakly non-linear waves in a prestressed thin elastic tube filled with an incompressible layered fluid, where the outer layer is assumed to be inviscid whereas the cylindrical core is considered to be viscous. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is studied. The governing equation is shown to be the perturbed Korteweg-de Vries (KdV) equation. A travelling wave type of solution for this evolution equation is sought and it is shown that the amplitude of the solitary wave for the perturbed KdV equation decays slowly with time.