Discrete instability in nonlinear lattices

The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order, strictly discrete, modulational instability (disappearing in the continuous envelope limit) above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion. Applied to the electrical lattice [Phys. Rev. E 51, 6127 (1995)], this accurately explains the experimental instability at wave numbers beyond 1.25 rad cell(-1). The theory is also briefly discussed for the sine-Gordon and Toda lattices.