Validity of Korteweg-de-Vries Equation for Arterial Pulse Waves

摘要

Korteweg-de-Vries equation (KdV) is very popular tool to describe nonlinear waveform like cnoidal waves or solitons. The long waves within environments with weak dispersion are the object of it. Many authors recognize pulse waves (PW) in blood vessels as varieties of such nonlinear waves. Therefore, the solution of the problem of the dispersion for pulse waves is either solid scientific support or vice versa of this widespread viewpoint. This paper first presents the solution of above problem with methods of dimension analysis. This technique is utterly independent of assumptions that are backbone of KdV theory. The results of analysis show that the dispersion of PW depends just of two parameters. Both of them are proportional to wavenumber. The ratio of them is equal to large Reynolds number. Thus, we can keep only one of them. It is dimensionless wave number: u = 2 π D λ 1, where D is inner diameter of vessel, and λ is the wavelength. For our purposes important is the result about weak dispersion of pulse waves. The dependence of frequency vs. the wavenumber is almost linear with minor cubic adding. Pulse wave is quite long wave as it follows from dimensional analysis. Both these outcomes confirm the validity of KdV equation for pulse waves into blood vessels.