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

Abstract

We consider the Fermi–Pasta–Ulam-type systems that describe an infinite systems of particles with nonlocal interaction on a two dimensional lattice. The main result concerns the existence of periodic and solitary traveling waves solutions. By means of critical point theory, sufficient conditions for the existence of such solutions are obtained.