Title: Modulational instability and chaotic-like behaviors in repulsive lattices

Abstract

In this work we study the dynamics of modulated waves in a mono atomic granular medium. We start by comparing each grain of the medium to a ball, and the interaction between various balls like linear elastic interactions we established that the dynamics of the system of pendulum used by Fermi-Pasta-Ulam can be governed by a discrete nonlinear Schrödinger equation. Like second advanced, we also established under which conditions this system could be prone to a modulational instability. The long-time dynamics of modulated waves is examined using numerical simulations which are corroborated with analytical results leads to the generation of nonlinear modulated waves which have the shape of a soliton.