Modulation of Nonlinear Waves in an Inviscid Fluid (Blood) Contained in a Stenosed Artery - Yaan, Yee Choy; Kim, Gaik Tay; Chee, Tiong Ong (HIKARI Ltd, 2013)
In this study, we have contributed to the derivation of mathematical model for the nonlinear waves modulation in an artery with the presence of a stenosis. Assume that the artery as an incompressible, prestressed thin walled elastic tube with a symmetrical stenosis and the blood as an incompressible inviscid fluid. Such a combination of a solid and fluid is considered to be a model for blood flow in a stenosed artery. By employing the nonlinear equations of tube and fluid as well as the knowledge of reductive perturbation method, we obtained the nonlinear Schr¨odinger (NLS) equation with variable coefficient as the governing equation for this model. Our results show that the solitary wave with the amplitude of one unit propagates to the left as travelling wave profile, ξ increases by preserving its bell-shape wave. As might be expected from physical consideration, the wave speed reaches its maximum value at the center of the stenosis and gets smaller and smaller as goes away from the center of the stenosis.