Journal of Mathematics and Statistics

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

Yaan Yee Choy, Kim Gaik Tay and Chee Tiong Ong

DOI : 10.3844/jmssp.2013.256.261

Journal of Mathematics and Statistics

Volume 9, Issue 3

Pages 256-261

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.

Copyright

© 2013 Yaan Yee Choy, Kim Gaik Tay and Chee Tiong Ong. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.