Often in linear stability investigations, growing standing waves are obtained. In this paper the important question is asked how the consideration of nonlinearities influences this growth and, in particular, whether a stabilization due to the nonlinear effects is possible.
The physical setting is wave propagation in an inextensible elastic solid. The three different types of modes mentioned in the paper title are studied, and it is shown that quite substantial differences in their behaviour, among others growing and decaying of amplitudes and the formation of shocks, are possible.
In this nicely written interesting paper analytic results from a perturbation analysis and a number of numeric results are presented.