In this article we propose a reduced model of the input-output behaviour of an arterial compartment, including the short systolic phase where wave phe- nomena are predominant. The objective is to provide basis for model-based signal processing methods for the estimation from non-invasive measure- ments and the interpretation of the characteristics of these waves. Due to phenomena such that peaking and steepening, the considered pressure pulse waves behave more like solitons generated by a Korteweg de Vries (KdV) model than like linear waves. So we start with a quasi-1D Navier-Stokes equation taking into account radial acceleration of the wall : the radial acceleration term being supposed small, a multiscale singular perturbation technique is used to separate the fast wave propagation phenomena taking place in a boundary layer in time and space described by a KdV equa- tion from the slow phenomena represented by a parabolic equation leading to two-elements windkessel models. Some particular solutions of the KdV equation, the 2 and 3-soliton solutions, seem to be good candidates to match the observed pressure pulse waves. Some very promising preliminary com- parisons of numerical results obtained along this line with real pressure data are shown.