Research Article Open Access

SOLITARY WAVE MODULATION IN AN ARTERY WITH STENOSIS FILLED WITH A VISCOUS FLUID

Yaan Yee Choy1, Kim Gaik Tay1 and Chee Tiong Ong2
  • 1 Universiti Tun Hussein Onn Malaysia, Malaysia
  • 2 Universiti Teknologi Malaysia, Malaysia

Abstract

In this study, the derivation of mathematical model for the wave modulation through an incompressible viscous fluid contained in a prestressed thin stenosed elastic tube is presented. The artery is assumed to be incompressible, prestressed thin walled elastic tube with a symmetrical stenosis, whereas the blood is considered to be incompressible and Newtonian fluid. By utilizing the nonlinear equations of tube and fluid, the weakly nonlinear wave modulation in such a medium is examined. Employing the reductive perturbation method and considering the long-wave approximation, we showed that the third-order term in the perturbation expansion is governed by the dissipative nonlinear Schrodinger equation with variable coefficient. Our results shown that this type of equation admits a downward bell-shape wave propagates to the right as time increases with decreasing wave amplitude.

Journal of Mathematics and Statistics
Volume 9 No. 3, 2013, 256-261

DOI: https://doi.org/10.3844/jmssp.2013.256.261

Submitted On: 29 July 2013 Published On: 4 September 2013

How to Cite: Choy, Y. Y., Tay, K. G. & Ong, C. T. (2013). SOLITARY WAVE MODULATION IN AN ARTERY WITH STENOSIS FILLED WITH A VISCOUS FLUID. Journal of Mathematics and Statistics, 9(3), 256-261. https://doi.org/10.3844/jmssp.2013.256.261

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Keywords

  • Tube
  • Newtonian Fluid
  • Wave Modulation
  • Nonlinear Schrodinger Equation