LAUSR

Abstract Travelling wave solutions of the front, kink or shock wave type are obtained analytically for one–dimensional viscoelastic Burgers equations with an objective Gordon–Schowalter time derivative in the constitutive law by means of a novel formulation based on changes of the independent and dependent variables that reduces the number of parameters to three. It is shown that, for the upper– and lower–convected Maxwell and Jaumann time derivatives, the thickness of the shock wave decreases as a nondimensional relaxation parameter is increased and that the velocity profiles for the Jaumann and lower–convected derivatives evolve from a sigmoid shape to linear piecewise ones as the relaxation parameter is increased. It is also shown that stress is a negative, even function that reaches a nil value at the upstream and downstream boundaries, and its width decreases as the relaxation parameter is increased for the Jaumann and upper–convected Maxwell derivatives. It is also reported that, at each location, the stress is larger for the lower–convected Maxwell derivative than for the Jaumann and upper–convected Maxwell derivatives.