Energy localization and transport in two-dimensional Fermi–Pasta–Ulam lattices

We investigate energy localization and transport in the form of discrete breathers and their movability in two-dimensional Fermi–Pasta–Ulam(FPU) lattices. We study the dynamics of the two-dimensional Fermi–Pasta–Ulam(FPU) lattice, incorporating the complicated effects of geometry, long-range interactions as well as nonlinear dispersion. We obtain several exact discrete breather(DB) solutions, such as the odd-parity and even-parity DBs, compact-like DBs and moving DBs for various geometries of the two-dimensional FPU chain. We show that DBs also exist in the same lattice in presence of next-nearest neighbour interaction. Large-amplitude exact subsonic travelling kink-soliton solutions are obtained in such a periodic chain in presence of long-range nonlinear dispersive interaction in the long-wavelength and weakly nonlinear limit. Such a two-dimensional FPU lattice admits finite amplitude nonlinear sinusoidal wave (NSW) solutions with short commensurate as well as incommensurate wavelengths for different geometries of the chain. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.