LOcalized modes on an Ablowitz-Ladik nonlinear impurity

TL;DR

This paper investigates localized modes caused by a nonlinear impurity in a one-dimensional lattice, providing exact solutions and analyzing how surface effects influence self-trapping and oscillations.

Contribution

It offers exact expressions for bound states and explores the impact of surface presence on nonlinear self-trapping phenomena.

Findings

Exact bound state profiles and energies derived.

Surface presence raises the nonlinearity threshold for self-trapping.

Localized modes exhibit high-amplitude oscillations at the 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.