nature [@craster2012acoustic; @Christensen2015MRCComunications; @srivastava2015elastic; @bertoldi2017flexible; @Kadi2019nrp]; and its pertinent progress in additive manufacturing techniques for creating these architectured materials [@raney2015].

In addition to the mathematical significance of their analysis, the study of solitary waves in mechanical systems shows also technological potential in impact mitigation [@yasuda2019origami], mechanical logic gates [@raney16], nondestructive testing [@nasrollahi2017], wave focusing [@deng2019focusing], and robot locomotion [@Deng2020sciadv]. The framework of these works is almost exclusively of discrete models, with only few results on elastic *continua*. A specific class of continuum that exhibits nonlinearities is of soft materials, whose microscopic composition and ability to sustain large deformations [@ogden97book] are the source of constitutive and geometrical nonlinearities, respectively. Thus, soft materials constitute a barely explored platform to theoretically study solitary waves, and in turn experimentally realize using current 3D printing capabilities [@Bandyopadhyay2015MRS; @Truby2016; @GARCIA2019am].

To the best of our knowledge, the first numerical observation of one-dimensional solitary waves in elastic *periodic* continua was by @leveque2002finite and @bale2002siam, using a finite-volume method they developed, which was followed by the studies of @yong2003solitary [@andrianov2013dynamic; @andrianov2014numerical; @navarro2015nature; @hussein2018nonlinear] and the references therein. As explained in these works, the periodicity of the media causes dispersion, whose balance with geometrical and constitutive nonlinearities forms elastic 