Rarefactive lattice solitary waves with high-energy sonic limit

We compute rarefactive solitary wave solutions in a nonlinear lattice with nearest-neighbor interaction forces that are sublinear near the undeformed state. This setting includes bistable bonds governed by a double-well potential. In contrast to the prototypical Korteweg-de Vries-type delocalization, the obtained solutions feature a nontrivial sonic limit (Chapman-Jouguet regime) with nonzero energy and algebraic decay at infinity. In the bistable case the waves are strongly localized and have high energy over the entire velocity range. Direct numerical simulations suggest stability of the computed solitary waves. We consider several quasicontinuum models that mimic some features of the obtained solutions, including the nontrivial nature of the sonic limit, but fail to accurately approximate their core structure for all velocities in the bistable regime.