On a variable-coefficient Korteweg-de Vries model in fluid-filled elastic tubes

In this paper we investigate a variable-coefficient Korteweg-de Vries (vcKdV) model in arterial mechanics. A new Lax pair of the vcKdV model is constructed, based on which the Bäcklund transformation, solitonic and some other solutions of the vcKdV model are obtained. With symbolic computation, the influence of the variable coefficients on solitonic propagation is investigated based on the solitonic solution, which has the following three aspects: (i) the coefficient of the nonlinear term affects the solitonic amplitude; (ii) the coefficient of the dispersive term controls the solitonic velocity and propagation trace; (iii) the coefficient of the dissipative term acts on both the solitonic amplitude and the velocity. We also analyze the variations of velocity and pressure of blood flow along the scaled axial coordinate after the static deformation in the vicinity of stenosis.