Discrete instability in nonlinear lattices

TL;DR

This paper analyzes how nonlinear discrete systems become unstable at certain amplitudes and wave numbers, explaining experimental results in electrical lattices and discussing applications to sine-Gordon and Toda lattices.

Contribution

It introduces a discrete multiscale analysis to predict modulational instability thresholds in nonlinear lattices, providing a theoretical explanation for experimental observations.

Findings

Identifies a threshold amplitude for instability in nonlinear discrete systems.

Accurately explains experimental instability in electrical lattices beyond wave number 1.25.

Discusses applicability to sine-Gordon and Toda lattice models.

Abstract

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