2006/04/19 by Imran A Butt, Jonathan A. D. Wattis, Jonathan A D Wattis
Computer Science · Mathematics · Physics and Astronomy · #Amplitude #Boundary value problem #Breather #Condensed matter physics #Geometry #Lattice (music) #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Scalar (mathematics) #Wavenumber #nlin.PS
paper · pdf · doi:10.1088/0305-4470/39/18/013
29 pages, 14 Figures
openalex publication_date 2006/04/19 · arxiv created 2006/12/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 generalized (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 not go to zero with the amplitude; we find that the energy threshold is maximized by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached.