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

Butt, Imran A and Wattis, Jonathan AD (2006) Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice. Journal of Physics. A, Mathematical and General, 39 . pp. 4955-4984. ISSN 0305-4470

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## Abstract

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached.

Item Type: Article Faculty of Science > School of Mathematical Sciences 932 Wattis, Jonathan 14 Aug 2008 16:52 24 Jun 2011 15:35

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