Periodic traveling wave solutions of discrete nonlinear Klein‐Gordon lattices

We prove the existence of periodic traveling wave solutions for general discrete nonlinear Klein-Gordon systems, considering both cases hard and soft on-site potentials. In case potentials, we implement a fixed-point theory approach, combining Schauder's theorem contraction mapping principle. This approach enables us to identify ring in energy space nontrivial exist, (norm) thresholds their existence, upper bounds on velocity. proof is facilitated by variational based mountain pass theorem. Thresholds averaged kinetic these exist are also derived.