English

Darboux transformations for linear operators on two dimensional regular lattices

Exactly Solvable and Integrable Systems 2010-04-19 v2 Mathematical Physics math.MP

Abstract

Darboux transformations for linear operators on regular two dimensional lattices are reviewed. The six point scheme is considered as the master linear problem, whose various specifications, reductions, and their sublattice combinations lead to other linear operators together with the corresponding Darboux transformations. The second part of the review deals with multidimensional aspects of (basic reductions of) the four point scheme, as well as the three point scheme.

Keywords

Cite

@article{arxiv.0905.3484,
  title  = {Darboux transformations for linear operators on two dimensional regular lattices},
  author = {Adam Doliwa and Maciej Nieszporski},
  journal= {arXiv preprint arXiv:0905.3484},
  year   = {2010}
}

Comments

23 pages, 3 figures, presentation improved

R2 v1 2026-06-21T13:04:38.421Z