Asymptotic dissipative waves in Jeffrey media from the point of view of double-scale method

This article studies previous results on nonlinear dissipative waves in Jeffrey media (viscoanelastic media without memory of order one) done by the first author, from the point of view of double scale method. For these media the equations of motion include second order derivative terms multiplied by a very small parameter. The physical meaning of a new (fast) variable, related to the surfaces across which the solutions or/and some of their derivatives vary steeply, is explained. The three-dimensional case is considered, that contains as a particular case an one-dimensional application worked out in a previous paper. Some known results are revised, other ones are derived and original. The thermodynamic models for Jeffrey media have applications in rheology and in other technological fields of applied sciences