We study localized modes on a single Ablowitz-Ladik impurity embedded in the bulk or at the surface of a one-dimensional linear lattice. Exact expressions are obtained for the bound state profile and energy. Dynamical excitation of the localized mode reveals exponentially-high amplitude oscillations of the spatial profile at the impurity location. The presence of a surface increases the minimum nonlinearity to effect a dynamical selftrapping.
@article{arxiv.0808.0456,
title = {LOcalized modes on an Ablowitz-Ladik nonlinear impurity},
author = {M. I. Molina},
journal= {arXiv preprint arXiv:0808.0456},
year = {2009}
}