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On nonlinear waves of the blood flow through arteries
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We discuss propagation of traveling waves in a blood filled elastic artery with an axially symmetric dilatation (an idealized aneurysm). The processes in the injured artery are modelled by equations for the motion of the wall of the artery and by equation for the motion of the fluid (the blood). For the case when long-wave approximation holds the model equations are reduced to a version of the perturbed Korteweg-deVries equation. Exact travelling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is discussed from the point of view of arterial mechanics.
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Cited by 2 Pith papers
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The Simple Equations Method (SEsM) and the use of exponential functions for obtaining simple and multisoliton solutions of some nonlinear partial differential equations
A generalized ansatz method (SEsM) is shown to reproduce Hirota's KdV multisoliton solutions and to yield an exact solution of a nonintegrable fifth-order KdV-type equation.
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Simple equations method (SEsM) and some of its numerous particular cases
The Simple Equations Method is a broad ansatz framework, and several established solution methods are shown to be particular cases, but the result is nearly tautological.
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