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

Butt, Imran A and Wattis, Jonathan AD (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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## Abstract

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 Fermi-Pasta-Ulam lattice, breathers Faculty of Science > School of Mathematical Sciences 924 Wattis, Jonathan 23 Jul 2008 15:37 23 Jun 2011 08:08

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