low-frequency, long-wavelength linear elastodynamics [@santosa1991dispersive], to find they serve as a lower bound to the velocity of solitary waves in the nonlinear settings. Our results thus generalize the findings of @yong2003solitary and @andrianov2014numerical, who showed that one-dimensional solitary waves in nonlinear laminates are supersonic[^2], similarly to the feature of solitary wave solutions to the KdV equation [@dauxois2006physics].

Lastly, we describe a procedure for determining which initial deformations will generate vector solitary waves. This is done using contour maps of the characteristic velocities as functions of the strain, identifying the initial strain and loading path in these maps, and employing a certain criterion regarding the gradient of the characteristic velocity along the path, as explained in detail later. These maps are also useful in identifying how the axial strain in the laminate changes during the propagation of the solitary waves. Specifically, we identify two domains in the map for quasi-pressure solitary waves, namely, a domain of solitary waves that tend to increase the axial strain in the laminate and a separate domain of solitary waves that tend to decrease the axial strain in the laminate. In accordance with this tendency, we term the latter *compressive* solitary waves, notwithstanding the fact that 