Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices
We consider the two-dimensional Fermi-Pasta-Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale analysis we reduce the governing lattice equations to...
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IOP
2014
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| Online Access: | https://eprints.nottingham.ac.uk/48080/ |
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| author | Wattis, Jonathan A.D. James, Lauren M. |
| author_facet | Wattis, Jonathan A.D. James, Lauren M. |
| author_sort | Wattis, Jonathan A.D. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We consider the two-dimensional Fermi-Pasta-Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale analysis we reduce the governing lattice equations to a nonlinear Schrodinger (NLS) equation coupled to a second equation for an accompanying slow mode. Two cases in which the latter equation can be solved and so the system decoupled are considered in more detail: firstly, in the case of a symmetric potential, we derive the form of moving breathers. We find an ellipticity criterion for the wavenumbers of the carrier wave, together with asymptotic estimates for the breather energy. The minimum energy threshold depends on the wavenumber of the breather. We find that this threshold is locally maximised by stationary breathers. Secondly, for an asymmetric potential we find stationary breathers, which, even with a quadratic nonlinearity generate no second harmonic component in the breather. Plots of all our findings show clear hexagonal symmetry as we would expect from our lattice structure. Finally, we compare the properties of stationary breathers in the square, triangular and honeycomb lattices. |
| first_indexed | 2025-11-14T20:07:49Z |
| format | Article |
| id | nottingham-48080 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:07:49Z |
| publishDate | 2014 |
| publisher | IOP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-480802020-05-04T16:52:36Z https://eprints.nottingham.ac.uk/48080/ Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices Wattis, Jonathan A.D. James, Lauren M. We consider the two-dimensional Fermi-Pasta-Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale analysis we reduce the governing lattice equations to a nonlinear Schrodinger (NLS) equation coupled to a second equation for an accompanying slow mode. Two cases in which the latter equation can be solved and so the system decoupled are considered in more detail: firstly, in the case of a symmetric potential, we derive the form of moving breathers. We find an ellipticity criterion for the wavenumbers of the carrier wave, together with asymptotic estimates for the breather energy. The minimum energy threshold depends on the wavenumber of the breather. We find that this threshold is locally maximised by stationary breathers. Secondly, for an asymmetric potential we find stationary breathers, which, even with a quadratic nonlinearity generate no second harmonic component in the breather. Plots of all our findings show clear hexagonal symmetry as we would expect from our lattice structure. Finally, we compare the properties of stationary breathers in the square, triangular and honeycomb lattices. IOP 2014-08-12 Article PeerReviewed Wattis, Jonathan A.D. and James, Lauren M. (2014) Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices. Journal of Physics A: Mathematical and Theoretical, 47 (34). 345101/1-345101/23. ISSN 1751-8121 nonlinear dynamics solitons discrete breathers lattices PACS numbers: 05.45.-a 05.45.Yv http://iopscience.iop.org/article/10.1088/1751-8113/47/34/345101/meta doi:10.1088/1751-8113/47/34/345101 doi:10.1088/1751-8113/47/34/345101 |
| spellingShingle | nonlinear dynamics solitons discrete breathers lattices PACS numbers: 05.45.-a 05.45.Yv Wattis, Jonathan A.D. James, Lauren M. Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices |
| title | Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices |
| title_full | Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices |
| title_fullStr | Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices |
| title_full_unstemmed | Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices |
| title_short | Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices |
| title_sort | discrete breathers in honeycomb fermi-pasta-ulam lattices |
| topic | nonlinear dynamics solitons discrete breathers lattices PACS numbers: 05.45.-a 05.45.Yv |
| url | https://eprints.nottingham.ac.uk/48080/ https://eprints.nottingham.ac.uk/48080/ https://eprints.nottingham.ac.uk/48080/ |