On integrable discretization of the inhomogeneous Ablowitz-Ladik model
solv-int
2009-10-31 v1 Exactly Solvable and Integrable Systems
Abstract
An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch oscillations are obtained. In particular, it is shown that the step of the discretization must be comensurable with the period of oscillations imposed by the inhomogeneous force. By proper choice of the step of the discretization the period of oscillations of a soliton in the discrete model can be made equal to an integer number of periods of oscillations in the underline continuous-time lattice.
Keywords
Cite
@article{arxiv.solv-int/9910004,
title = {On integrable discretization of the inhomogeneous Ablowitz-Ladik model},
author = {V. V. Konotop},
journal= {arXiv preprint arXiv:solv-int/9910004},
year = {2009}
}
Comments
6 pages, 1 figure, LaTeX