Onsite and offsite bound states of the discrete nonlinear Schrödinger equation and the Peierls–Nabarro barrier. (22nd December 2015) - Jenkinson, M; Weinstein, M I
Abstract: 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 of onsite 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 offsite 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 Peierls–Nabarro energy barrier.