Compactons and Chaos in Strongly Nonlinear Lattices

TL;DR

This paper investigates strongly nonlinear Hamiltonian lattices, revealing super-exponentially localized solitary waves called compactons, their nearly elastic collisions, and the emergence of chaos, with results applicable across energy scales.

Contribution

It introduces an accurate numerical method to find compactons for any nonlinearity index and characterizes their dynamics and chaotic behavior in strongly nonlinear lattices.

Findings

Solitary waves are super-exponentially localized.

Compactons evolve from general localized perturbations.

Chaotic states develop over long times in finite lattices.

Abstract

We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are super-exponentially localized, and present an accurate numerical method allowing to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically, nevertheless on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system's scaling, these dynamical properties are valid for any energy.