The Korteweg-de Vries-Burgers hierarchy in fluid-filled elastic tubes

In this work, contribution of higher order terms in modified reductive perturbation method is studied for the propagation of weakly nonlinear waves in fluid-filled elastic tubes. The basic set of equation of fluid and equation of tube is reduced to the Korteweg-de Vries-Burgers equation for the first order displacement component in the radial direction and a linear Korteweg-de Vries-Burgers inhomogeneous equation for the second order displacement component in the radial direction. Dynamical processes of the solitary waves have been numerically analyzed by solving the Korteweg-de Vries-Burgers equation for the first order and the linearized KdV-Burgers equation with an inhomogeneous equation for the second order using pseudo-spectral method.