On nonlinear waves of the blood flow through arteries

2016/12/24 by Елена Николова, Nikolova, Elena, Ivan P. Jordanov +3 · 1 citation
Mathematics · Physics and Astronomy · #Biological Physics (physics.bio-ph) #Differential Equations and Numerical Methods #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.1701.02371

openalex publication_date 2016/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• The Simple Equations Method (SEsM) and the use of exponential functions for obtaining simple and multisoliton solutions of some nonlinear partial differential equations

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