2014/05/15 by Michael J. Jenkinson, Michael I. Weinstein, Jenkinson, Michael +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Strong Light-Matter Interactions #cond-mat.mes-hall #math-ph #math.AP #math.MP #nlin.PS
paper · pdf · doi:10.48550/arxiv.1405.3892
to appear in Nonlinearity
openalex publication_date 2014/05/15 · arxiv created 2015/08/03 · arxiv updated 2015/08/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We construct multiple families of solitary standing waves of the discrete cubically nonlinear Schrödinger equation (DNLS) in dimensions d=1,2 and 3. These states are obtained via a bifurcation analysis about the continuum (NLS) limit. One family consists \it on-site symmetric (vertex-centered) states; these are spatially localized solitary standing waves which are symmetric about any fixed lattice site. The other spatially localized states are \it off-site symmetric. Depending on the spatial dimension, these may be bond-centered, cell-centered, or face-centered. Finally, we show that the energy difference among distinct states of the same frequency is exponentially small with respect to a natural parameter. This provides a rigorous bound for the so-called \it Peierls-Nabarro energy barrier.