Application of the (G′/G)-expansion method to nonlinear blood flow in large vessels

Abstract

As is widely known today, Navier–Stokes equations are used to describe blood flow in large vessels. In the past several decades, and even in very recent works, these equations have been reduced to Korteweg–de Vries (KdV), modified KdV or Boussinesq equations. In this paper, we avoid such simplifications and investigate the analytical traveling wave solutions of the one-dimensional generic Navier–Stokes equations, through the (G ' /G)-expansion method. These traveling wave solutions include hyperbolic functions, trigonometric functions and rational functions. Since some of them are not yet explored in the study of blood flow, we pay attention to hyperbolic function solutions and we show that the (G ' /G)-expansion method presents a wider applicability that allows us to bring out the widely known blood flow behaviors. The biological implications of the found solutions are discussed accordingly.