Nonlinear propagating localized modes in a 2D hexagonal crystal lattice
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.
Cite
@article{arxiv.1409.0355,
title = {Nonlinear propagating localized modes in a 2D hexagonal crystal lattice},
author = {J. Bajars and J. C. Eilbeck and B. Leimkuhler},
journal= {arXiv preprint arXiv:1409.0355},
year = {2020}
}
Comments
Both this paper and arXiv 1408.6853 discuss similar models with the same on-site potential. This paper has a Lennard-Jones interparticle potential, 1408.6853 has a piecewise polynomial function. The latter favours the existence of long-lived kinks, and much of 1408.6853 is given to a study of these. Both models support long-lived breathers, and the present paper concentrates on such solutions