internal mode of the solitary wave. Similar long-lived oscillations were reported before in other fields [@Campbell1983ty; @Mantsyzov1995pra; @kivshar1998internal; @Szankowski2010prl], and were also reported recently in an acoustic system that is described using the continuum limit of a discrete model based on mechanicalelectrical analogies [@zhang2017bright]. Our results are the first report of oscillating vector solitary waves that are generated from the equations of continuum elastodynamics.

Next, we characterize the relation between the amplitude of the strain and the velocity of the solitary waves. This is done for a wide range of initial conditions, which were carefully chosen to generate in each experiment a single solitary wave. These experiments show that the velocity is a monotonically increasing function of the amplitude. This observation agrees with the results of @ziv2019b, who generated trains of solitary waves from a single set of initial conditions, and observed that the taller waves in the train propagate faster than the shorter waves. Notably, this velocity-amplitude relation is opposite to the relation for the vector solitary waves in the discrete mechanical model of @deng2017 [@deng2019prl], there the waves with smaller amplitudes are faster. We also determine the velocity of Bloch-Floquet waves in the laminate in the limit of 