On modulational instability and energy localization in anharmonic lattices at finite energy density

TL;DR

This paper investigates how energy localizes in anharmonic lattices due to modulational instability, describing the process through continuum theory, soliton dynamics, and analytical predictions of time scales, supported by numerical results.

Contribution

It introduces a continuum theory for energy localization in anharmonic lattices, detailing the formation and merging of envelope solitons at finite energy density, a novel analytical approach.

Findings

Localization occurs via envelope solitons

Soliton merging leads to a single localized energy object

Analytical time scales match numerical simulations

Abstract

The localization of vibrational energy, induced by the modulational instability of the Brillouin-zone-boundary mode in a chain of classical anharmonic oscillators with finite initial energy density, is studied within a continuum theory. We describe the initial localization stage as a gas of envelope solitons and explain their merging, eventually leading to a single localized object containing a macroscopic fraction of the total energy of the lattice. The initial-energy-density dependences of all characteristic time scales of the soliton formation and merging are described analytically. Spatial power spectra are computed and used for the quantitative explanation of the numerical results.