Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Abstract

Abstract Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in, for example, variable-radius arteries. With respect to the nonlinear waves in an artery full of blood with certain aneurysm, pulses in a blood vessel, or features in a circulatory system, this paper symbolically computes out an auto-Bäcklund transformation via a noncharacteristic movable singular manifold, certain families of the solitonic solutions, as well as a family of the similarity reductions for a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers equation. Aiming, e.g., at the dynamical radial displacement superimposed on the original static deformation from an arterial wall, our results rely on the axial stretch of the injured artery, blood as an incompressible Newtonian fluid, radius variation along the axial direction or aneurysmal geometry, viscosity of the fluid, thickness of the artery, mass density of the membrane material, mass density of the fluid, strain energy density of the artery, shear modulus, stretch ratio, etc. We also highlight that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.