NLS Equation with a Variable Coefficient in a Stenosed Elastic Tube Filled with an Averaged Inviscid Fluid

Abstract

Wave modulation in an elastic tube has been studied by researchers since year 1979. In the present work, by considering the artery as a prestressed thin elastic tube with a symmetrical stenosis and the blood as an incompressible averaged inviscid fluid. We have studied the amplitude modulation of non-linear waves in such a composite medium by using the reductive perturbation method. The governing equations can be reduced to the non-linear Schrodinger (NLS) equation with variable coefficient. The progressive wave solution to the above non-linear evolution equation is then sought. The non-linear Schrodinger (NLS) equation with variable coefficient shows increasing shock wave propagates to the right as real time passed. Keywords: Elastic tube; stenosis; inviscid fluid; nonlinear Schrodinger equation. 2010 Mathematics Subject Classification: 35Q53