Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

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.

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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.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/1017252
Keywords: Fermi-Pasta-Ulam lattice, breathers
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Depositing User: Wattis, Jonathan
Date Deposited: 23 Jul 2008 14:37
Last Modified: 04 May 2020 20:28
URI: https://eprints.nottingham.ac.uk/id/eprint/924

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