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

Authors

  • Yaan Yee Choy
  • Chee Tiong Ong
  • Kim Gaik Tay

DOI:

https://doi.org/10.11113/matematika.v28.n.310

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

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Published

2012-06-01

Issue

Section

Mathematics