solitary waves. Only recently, this principle for generating solitary waves was tested by @ziv2019b in *two-dimensional* continuum elastodynamics. There, the authors have developed a designated finite-volume method to simulate finite motions of soft laminates whose displacement field consists of two coupled components. By application of this method to a periodic repetition of compressible layers that differ in their mass density, the authors were able to observe the formation of *vector* solitary wavessolitary waves with (at least) two components and two polarizations that are coupled one with the otherin this case, when the axial and transverse components of the displacement field are coupled. To the best of our knowledge, that was the first report of vector solitary waves in an elastic continuum, within the framework of nonlinear elastodynamics [@ogden97book]. An earlier report of such waves in a *discrete* mechanical medium was given by @deng2017 [@deng2019prl], who conceived a model made of rigid squares that are connected using linear springs at their corners, thereby allowing for two coupled degrees of freedom for the squares: rotation and translation. While both the systems considered by @deng2017 [@deng2019prl] and the system considered here are two-dimensional and nonlinear, there are fundamental differences between them, as we 