English

Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model

Pattern Formation and Solitons 2014-06-26 v1 Exactly Solvable and Integrable Systems

Abstract

We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schroedinger equation of Ablowitz and Ladik. When considered in the complex plane, these two solutions are identical. In the continuum limit, they reduce to known elliptic function solutions. In the long wave limit, the dark one reduces to the collision of two discrete dark solitons, and the bright one to a discrete breather.

Keywords

Cite

@article{arxiv.nlin/0509005,
  title  = {Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model},
  author = {K. W. Chow and Robert Conte and Neil Xu},
  journal= {arXiv preprint arXiv:nlin/0509005},
  year   = {2014}
}

Comments

12 pages, 2 figures. To appear, Physics Letters A

R2 v1 2026-07-22T18:14:17.421Z