the homogeneous medium can be used to predict quasi-pressure solitary waves in a soft laminate with a periodic modulation in its mass density. This result relies on the fact that Eq.$\ $ is independent of the mass density, and hence turns useful in the solution of a laminate whose only modulation is in that property.

Fig.$\ $\[fig:Characterization\](b) mirrors the presentation in panel a for quasi-shear solitary waves. Since in this case the profile changes between different cells, we present our results in the following way. First, we have calculated the maximal values of $\shearstrain$ and $\pressurestrain$ over the time that the solitary wave traverses a unit cell, as we previously did for the quasi-pressure waves. Since now different layers exhibit different maximal values owing to the internal mode, we here present the average value. Specifically, the average of the values for phase $a$ (resp.$\ $$b$) is taken over the number of layers within one period of the oscillation; the average is denoted by the disc (resp.$\ $diamond) markers. As in panel (a), to the results from the full-wave simulations we add in black curves the solutions of Eq.$\ $, when subjected to the compatibility conditions . Here again, the markers 