Solitary traveling waves in Fermi-Pasta-Ulam-type systems with nonlocal interaction on a 2D lattice

The article deals with the Fermi-Pasta-Ulam-type systems that describe an infinite system of particles with nonlocal interaction on a two-dimensional lattice. It is assumed that every particle interacts nonlinearly with several of its horizontal and vertical neighbors. The main result concerns the existence of solitary traveling-wave solutions with vanishing relative displacement profiles. By means of the critical point theory, sufficient conditions for the existence of such solutions have been obtained.