In this paper, the propagation of pulse wave in a deformable elastic vessel filled with inviscid blood is studied. Starting from the stress–strain relationship of blood vessel wall, momentum conservation equation and the Naiver–Stokes equation, the basic equations describing the wall motion and blood flow are established. By utilizing reductive perturbation technique and long wave approximation theory, the basic equations are simplified into a classical third-order mKdV equation with variable coefficients. In order to describe the propagation characteristics of pulse wave more accurately, a fifth-order variable-coefficient mKdV equation is derived. Then, the tanh-function method is applied to find the localized traveling wave solutions of these equations. Based on these localized traveling wave solutions, we further investigate the effects of higher order terms and initial vessel deformation on the characteristics of pulse wave propagation, blood flow velocity and the volume of blood flow. The results show that the higher-order nonlinear and dispersion terms lead to the distortion of the wave, while the initial deformation of the tube wall will influence the wave amplitude and wave width.

本文研究了脉搏波在充满无粘性血液的可变形弹性血管中的传播。从血管壁的应力-应变关系、动量守恒方程和Naiver-Stokes方程出发，建立了描述血管壁运动和血流的基本方程。利用约简微扰技术和长波近似理论，将基本方程简化为经典的变系数三阶mKdV方程。为了更准确地描述脉搏波的传播特性，推导出五阶变系数mKdV方程。然后，应用 tanh 函数方法来找到这些方程的局部行波解。基于这些局部行波解决方案，我们进一步研究了高阶项和初始血管变形对脉搏波传播特性、血流速度和血流量的影响。结果表明，高阶非线性项和色散项导致波的畸变，而管壁的初始变形会影响波幅和波宽。