Vector Nonlinear Klein-Gordon Lattices: General Derivation of Small Amplitude Envelope Soliton Solutions

Group velocity and group velocity dispersion for a wave packet in vectorial discrete Klein-Gordon models are obtained by an expansion, based on perturbation theory, of the linear system giving the dispersion relation and the normal modes. We show how to map this expansion on the Multiple Scale Expansion in the real space and how to find Non Linear Schr\"odinger small amplitude solutions when a nonlinear one site potential balances the group velocity dispersion effect.