English

Algebraic entropy, symmetries and linearization of quad equations consistent on the cube

Exactly Solvable and Integrable Systems 2016-03-28 v1 Mathematical Physics math.MP

Abstract

We discuss the non autonomous nonlinear partial difference equations belonging to Boll classification of quad graph equations consistent around the cube. We show how starting from the compatible equations on a cell we can construct the lattice equations, its B\"acklund transformations and Lax pairs. By carrying out the algebraic entropy calculations we show that the H4H^4 trapezoidal and the H6H^6 families are linearizable and in a few examples we show how we can effectively linearize them.

Keywords

Cite

@article{arxiv.1603.07930,
  title  = {Algebraic entropy, symmetries and linearization of quad equations consistent on the cube},
  author = {Giorgio Gubbiotti and Christian Scimiterna and Decio Levi},
  journal= {arXiv preprint arXiv:1603.07930},
  year   = {2016}
}