English

On an integrable discretisation of the Ablowitz-Ladik hierarchy

Exactly Solvable and Integrable Systems 2014-01-27 v1

Abstract

Following the general results on the relationships about Backlund transformations (BTs) and exact discretisation given in a previous work [12], we consider the Ablowitz-Ladik hierarchy and a corresponding family of BTs. After discussing the boundary conditions, we show how to get explicit transformations. The Hamiltonian properties of the maps and of the discrete flows are examined. The conditions on the parameters of the map giving exact discretisations are discussed. Finally, analytical and numerical examples are given.

Keywords

Cite

@article{arxiv.1303.1639,
  title  = {On an integrable discretisation of the Ablowitz-Ladik hierarchy},
  author = {Federico Zullo},
  journal= {arXiv preprint arXiv:1303.1639},
  year   = {2014}
}

Comments

18 pages, 2 figures. Submitted to Inverse Problems. Supported by an INdAM-COFUND Fellowship