SOLITARY WAVES IN PRESTRESSED ELASTIC TUBES

In this work, we studied the propagation of non-linear waves in a pre- stressed thin elastic tube filled with an inviscid fluid. In the analy sis, analogous to the physiological conditions of the arteries, the tu be is assumed to be subject to a uniform pressure P-0 and a constant a xial stretch ratio lambda(z). In the course of blood flow it is assume d that a large dynamic displacement is superimposed on this static fie ld. Furthermore, assuming that the displacement gradient in the axial direction is small, the non-linear equation of motion of the tube is o btained. Using the reductive perturbation technique, the propagation o f weakly non-linear waves in the long-wave approximation is investigat ed. It is shown that the governing equations reduce to the Korteweg-de Vries equation which admits a solitary wave solution. The result is di scussed for some elastic materials existing in the literature.