Nonlinear propagating localized modes in a 2D hexagonal crystal lattice

TL;DR

This study investigates nonlinear localized modes in a 2D hexagonal crystal lattice, confirming the existence of long-lived propagating breathers and exploring their frequency localization, contributing to understanding of exact solutions in physical lattices.

Contribution

The paper extends a 2D hexagonal lattice model to include arbitrary atomic interactions and out-of-cell atom movement, providing detailed numerical evidence of propagating discrete breathers.

Findings

Confirmed existence of long-lived propagating breathers

Observed localization of energy in frequency space

Contributed to the understanding of exact moving breather solutions

Abstract

In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marin, Eilbeck and Russell in 1998. We perform a detailed numerical study of nonlinear propagating localized modes, that is, propagating discrete breathers and kinks. The original model is extended to allow for arbitrary atomic interactions, and to allow atoms to travel out of the unit cell. A new on-site potential is considered with a periodic smooth function with hexagonal symmetry. We are able to confirm the existence of long-lived propagating discrete breathers. Our simulations show that, as they evolve, breathers appear to localize in frequency space, i.e. the energy moves from sidebands to a main frequency band. Our numerical findings contribute to the open question of whether exact moving breather solutions exist in 2D hexagonal layers in physical crystal lattices.