A note on traveling wave solutions for a class of nonlinear viscoelastic media

Traveling wave solutions (TWSs) are investigated for transverse propagation in a class of nonlinear viscoelastic media. Specifically, the propagation speed and shock thickness are determined, it is shown that vortex sheet formation occurs as the Reynolds number tends to infinity, and a special case exact solution is obtained and analyzed. Most significantly, it is proved that stable, transverse TWSs are possible only in super-Hookean media (i.e., media in which the fourth elastic modulus is positive) and that the propagation speed is a minimum when the limit at +∞ is zero.