Periodic traveling waves in a discrete Klein-Gordon lattice system with mutual nonlinear coupling

This paper is devoted to the study of the existence and asymptotic behavior of periodic traveling wave solutions in a discrete Klein-Gordon lattice system with mutual nonlinear coupling. We first show the existence of nontrivial periodic traveling wave solutions for the coupled system via variational methods. Furthermore, we investigate the asymptotic behavior of these solutions. Using a monotonicity method, we show that these solutions converge to a periodic traveling wave solution of the corresponding decoupled system as the mutual coupling coefficient tends to zero.