As a nonlinear alternative to the linear interpretation of arterial blood pressure waveform, soliton theory has been proposed to model arterial blood pressure by interpreting the pulsatile nature of pressure pulses in the viewpoint of soliton transmission. The existing solitary wave literature supports this interpretation by deriving Korteweg-de Vries (KdV) type dynamics from 1-D Navier-Stokes equations. In this paper, we explain and discuss the derivation of KdV type dynamics for arterial blood pressure from basics of fluid motion. As original work, we provide two verification tests for two of the existing KdV models in three case studies which are considered to be interconnected sections of a simplified arterial network. Finally,
using both KdV models and considering realistic inlet boundary conditions, we study arterial blood pressure waveforms using nonlinear Fourier analysis to extract physical information.