Existence of subsonic periodic traveling waves in discrete Klein-Gordon type equations with nonlocal interaction

The article deals with the discrete Klein-Gordon type equations that describe infinite chains of linearly coupled nonlinear oscillators with nonlocal interactions. It is assumed that each oscillator interacts with several of its neighbors on both sides. The main result concerns the existence of subsonic periodic traveling wave solutions in such equations. Sufficient conditions for the existence of such waves are established using the variational method and the linking theorem.