Resumen
The aim of this paper is to provide a construction of travelling waves in an extended one-dimensional lattice model with non-nearest neighbour interactions. These models, coming mainly from solid state physics, are known to play an important role in the mechanisms of propagation of energy. We focus on an extended version of the Klein–Gordon chains, i.e. each particle is embedded into an an-harmonic potential and linearly coupled to their first and second neighbours. We use the technique of reduction to a finite-dimensional centre manifold to prove the existence of travelling waves of several types and investigate the role played by the interaction to second nearest neighbours.