Discrete breathers in honeycomb FermiPastaUlam lattices
Abstract
We consider the twodimensional FermiPastaUlam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalarvalued quantity subject to nearest neighbour interactions. Using multiplescale analysis we reduce the governing lattice equations to a nonlinear Schrödinger 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 maximized 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 August 2014
 DOI:
 10.1088/17518113/47/34/345101
 arXiv:
 arXiv:1407.2828
 Bibcode:
 2014JPhA...47H5101W
 Keywords:

 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 to appear in J Phys A