Dressed solitary waves in thick-walled elastic tubes

Abstract

In the present work, by using the approximate nonlinear equations of an incompressible inviscid fluid contained in a prestressed thick elastic tube, the propagation of a localized travelling wave solution in such a medium is investigated. Employing the hyperbolic tangent method and considering the long-wave limit, we showed that the lowest-order term in the perturbation expansion gives a solitary wave equivalent to the localized travelling wave solution of the Korteweg-de Vries equation. The solitary wave type of solution is also given for the second-order terms in the perturbation expansion. The correction terms in the speed of propagation are also obtained as a part of the solution of perturbation equations. The possible application of the present solution to blood flow problems in arteries is also discussed.