English

On a nonlinear integrable difference equation on the square 3D-inconsistent

Exactly Solvable and Integrable Systems 2009-04-28 v2

Abstract

We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra differential-difference equations. This equation is not symmetric with respect to the exchange of the two discrete variables and does not satisfy the 3D-consistency condition necessary to belong to the Adler-Bobenko-Suris classification. Its integrability is proved by constructing its Lax pair.

Cite

@article{arxiv.0902.2126,
  title  = {On a nonlinear integrable difference equation on the square 3D-inconsistent},
  author = {D. Levi and R. I. Yamilov},
  journal= {arXiv preprint arXiv:0902.2126},
  year   = {2009}
}
R2 v1 2026-06-21T12:10:50.900Z