Atomic-scale localization of high-energy solitary waves on lattices

One-dimensional monatomic lattices with Hamiltonian H=∑n∈Z((1/2)pn2+V(qn+1−qn)) are known to carry localized travelling wave solutions for generic nonlinear potentials V [Comm. Math. Phys. 161 (1994) 391]. In this paper we derive the asymptotic profile of these waves in the high-energy limit H→∞ for Lennard–Jones type interactions. The limit profile is proved to be a universal, highly discrete, piecewise linear wave concentrated on a single atomic spacing. This shows that dispersionless energy transport in these systems is not confined to the long-wave regime on which the theoretical literature has hitherto focused, but also occurs at atomic-scale localization.