Localized modes on an Ablowitz–Ladik nonlinear impurity

Abstract: 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. [Copyright &y& Elsevier]