Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice
We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support s...
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| Format: | Article |
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IOP
2007
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| Online Access: | https://eprints.nottingham.ac.uk/924/ |
| _version_ | 1848790503440515072 |
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| author | Butt, Imran A. Wattis, Jonathan A.D. |
| author_facet | Butt, Imran A. Wattis, Jonathan A.D. |
| author_sort | Butt, Imran A. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice
with hexagonal symmetry. Using asymptotic methods based on
small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers
are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, symptotic estimates for the breather energy,
and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt \& Wattis, {\em J Phys A}, {\bf 39}, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation. |
| first_indexed | 2025-11-14T18:13:39Z |
| format | Article |
| id | nottingham-924 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:13:39Z |
| publishDate | 2007 |
| publisher | IOP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-9242020-05-04T20:28:42Z https://eprints.nottingham.ac.uk/924/ Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice Butt, Imran A. Wattis, Jonathan A.D. We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, symptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt \& Wattis, {\em J Phys A}, {\bf 39}, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation. IOP 2007 Article PeerReviewed Butt, Imran A. and Wattis, Jonathan A.D. (2007) Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice. J Phys A Theor Gen, 40 . pp. 1239-1264. Fermi-Pasta-Ulam lattice breathers |
| spellingShingle | Fermi-Pasta-Ulam lattice breathers Butt, Imran A. Wattis, Jonathan A.D. Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice |
| title | Discrete breathers in a two-dimensional
hexagonal Fermi-Pasta-Ulam lattice |
| title_full | Discrete breathers in a two-dimensional
hexagonal Fermi-Pasta-Ulam lattice |
| title_fullStr | Discrete breathers in a two-dimensional
hexagonal Fermi-Pasta-Ulam lattice |
| title_full_unstemmed | Discrete breathers in a two-dimensional
hexagonal Fermi-Pasta-Ulam lattice |
| title_short | Discrete breathers in a two-dimensional
hexagonal Fermi-Pasta-Ulam lattice |
| title_sort | discrete breathers in a two-dimensional
hexagonal fermi-pasta-ulam lattice |
| topic | Fermi-Pasta-Ulam lattice breathers |
| url | https://eprints.nottingham.ac.uk/924/ |