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Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices

Wattis, Jonathan A.D.; James, Lauren M.

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Authors

JONATHAN WATTIS jonathan.wattis@nottingham.ac.uk
Professor of Applied Mathematics

Lauren M. James



Abstract

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.

Citation

Wattis, J. A., & James, L. M. (2014). Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices. Journal of Physics A: Mathematical and Theoretical, 47(34), Article 345101. https://doi.org/10.1088/1751-8113/47/34/345101

Journal Article Type Article
Acceptance Date Jul 4, 2014
Publication Date Aug 12, 2014
Deposit Date Nov 13, 2017
Publicly Available Date Nov 13, 2017
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 47
Issue 34
Article Number 345101
DOI https://doi.org/10.1088/1751-8113/47/34/345101
Keywords nonlinear dynamics, solitons, discrete breathers, lattices
PACS numbers: 05.45.-a, 05.45.Yv
Public URL https://nottingham-repository.worktribe.com/output/734305
Publisher URL http://iopscience.iop.org/article/10.1088/1751-8113/47/34/345101/meta

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