Almost compact breathers in anharmonic lattices near the continuum limit

Certain strictly anharmonic one-dimensional lattices support discrete breathers over a macroscopic localized domain that in the continuum limit becomes exactly compact. The discrete breather tails decay at a double-exponential rate, so such systems can store energy locally, especially since discrete breathers appear to be stable for amplitudes below a sharp stability threshold. The effective width of other solutions broadens over time, but, under appropriate conditions, only after a positive waiting time. The continuum limit of a planar hexagonal lattice also supports a compact breather.