associated to the laminate either coincide or fall very close to these curves.

To highlight the oscillatory nature of the wave amplitude, we present in the inset of Fig.$\ $\[fig:Characterization\](b) the values over which the average was obtained for two exemplary markers; each point in the inset corresponds to a different layer that was used in the calculation of the average, where the number of three arbitrary layers is displayed. The slow spatial modulation in the wave profile that appears in Fig.$\ $\[fig:SolitonShear\] manifests itself here as closed ellipses, showing how the amplitude oscillates periodically about a mean. Interestingly, the orientations of the ellipses associated with each phase are opposite one to another.

The dependency of the velocity on the amplitude is shown in Fig.$\ $\[fig:velocities\](a) by plotting the velocity of quasi-pressure solitary waves as function of the maximal value of $\pressurestrain$ in phase $a$ over the time that the solitary wave traverses a unit cell. Here again, the cyan, red and green markers correspond to waves that were generated with $\initial{\shearstrain}=2,2.2$ and $2.4$, respectively. We observe that the highest and lowest clusters correspond to the largest and smallest $\initial{\shearstrain}$, respectively. We furthermore observe that within each cluster, markers at 