Nonlinear propagating localized modes in a 2D hexagonal crystal lattice

Janis Bajars, John Christopher Eilbeck, Benedict Leimkuhler

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40 Citations (Scopus)
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In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marín, 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 shed light on the open question of whether exact moving breather solutions exist in 2D hexagonal layers in physical crystal lattices.

Original languageEnglish
Pages (from-to)8-20
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Early online date18 Mar 2015
Publication statusPublished - May 2015


  • 2D mobile discrete breathers
  • Intrinsic localized modes
  • Kinks
  • Propagating excitations


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