in adjacent cell, we find that its velocity is constant and equal for both phases; this wave is therefore a solitary wave. More specifically, since the solitary wave exhibits coupling between its axial and transverse components and polarizations, it is a *vector* solitary wave. To the best of our knowledge, these vector solitary waves were first observed by @ziv2019b using numerical experiments. Here, we carry out a comprehensive characterization of the possible vector solitary waves in the medium.

We first observe that the wave couples axial and shear strains of an identical sign, similarly to quasi-pressure waves in a homogeneous compressible Gent medium (Fig.$\ $\[fig:integralCurves\]a). Hence, we associate the solitary wave with a quasi-pressure mode, and term it a quasi-pressure solitary wave. To facilitate the identification of these features, we show in Fig.$\ $\[fig:pressureSoliton\](b) the corresponding axial (left panel) and shear (right panel) strains at the center of selected layers made of phase $a$, as functions of time. Arbitrarily, we chose each $6^{\mathrm{th}}$ layer from the range $64\leq n\leq88$; each curve corresponds to a different layer whose number appears on top of the curve. Evidently, the shape is maintained, and the equal spacing between the curves confirms that the velocity 