is constant too. Furthermore, we observe that the wave profile is reminiscent of the sech$^{2}$ profile, which, as mentioned, is the solitary wave profile associated with the well-known KdV equation [@korteweg1895xli]. This wave profile was also obtained for one-dimensional solitary waves in a laminate, using an asymptotic homogenization method [@andrianov2014numerical]. A comparison between the wave profile at $n=76$ and the sech$^{2}$ functions $$\pressurestrain=0.154\mathrm{sech}^{2}\left(1.33t\right),\ \shearstrain=2.2+0.108\mathrm{sech^{2}}\left(1.33t\right)\label{eq:sech-1}$$ (plotted in red dash), demonstrates the agreement between them.

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Fig.$\ $\[fig:SolitonShear\](a) shows the distribution of the axial (left panel) and shear (right panel) strains as functions of space and time, when the laminate is pre-strained according to the parameters

$$\initial{\shearstrain}=2.2,\ \initial{\pressurestrain}=0,\ \amp{\shearstrain}=0.5,\ \amp{\pressurestrain}=-0.5,\ w=0.08\,\mathrm{m}.\label{eq:quasi-shear-strains}$$

We observe that a rightward propagating wave is generated, as also depicted in movie S2 in the supplementary material, with the following features. First, by examining the wave profile, we find that in contrast with quasi-pressure waves, here (*i*) the time dependency of the waves across each layer is not a sech$^{2}$ functionnor any other symmetric function; (*ii*) the wave profile changes not only between the different phases, but also between adjacent unit cells. The latter change in the profile occurs in a periodic manner without dispersing in time.

Second, by 