Nonlinear waves in a stenosed elastic tube filled with viscous fluid: Forced perturbed korteweg-de vries equation
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CitationGaik, T. K., Demiray, H. & Tiong, O. C. (2008). Nonlinear waves in a stenosed elastic tube filled with viscous fluid: Forced perturbed korteweg-de vries equation. Springer, 12(), 157-163. doi:10.1007/978-1-4020-9100-1_16
In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By introducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the smallness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.
SourceSpringer Proceedings in Physics
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