Exact compact breather-like solutions of two-dimensional Fermi-Pasta-Ulam lattice

We demonstrate that two-dimensional Fermi-Pasta-Ulam lattice support exact discrete compact breather-like solutions. We also find exact compact breather solutions of the same lattice in presence of long-range interaction with r(-s) dependence on the distance in the continuum limit. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.