On some nonlinear waves in fluid-filled viscoelastic tubes: weakly dispersive case

By employing the nonlinear equations of motion of an incompressible, isotropic and prestressed thin viscoelastic tube and the approximate equations of an incompressible inviscid fluid, we studied the existence of some possible evolution equations in the long-wave approximation and their progressive wave solutions. It is shown that, depending on the set of values of the initial deformation, it is possible to obtain the modified Burgers, the modified KdV and the modified KdV-Burgers equations. A set of progressive wave solutions is presented for such evolution equations. It is observed that for all these modified evolution equations the wave speeds are proportional to the square of the wave amplitude.