On the derivation of some non-linear evolution equations and their progressive wave solutions

In the present work, utilizing the reductive perturbation method, the non-linear equations of a prestressed viscoelastic thick tube filled with a viscous fluid are examined in the longwave approximation and some evolution equations and their modified forms are derived. The analytical solution of some of these equations are obtained and it is shown that for perturbed cases, the wave amplitude and the phase velocity decay in the time parameter.