Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation
Abstract
In this paper we construct a non-autonomous version of the Hietarinta equation [Hietarinta J., J. Phys. A: Math. Gen. 37 (2004), L67-L73] and study its integrability properties. We show that this equation possess linear growth of the degrees of iterates, generalized symmetries depending on arbitrary functions, and that it is Darboux integrable. We use the first integrals to provide a general solution of this equation. In particular we show that this equation is a sub-case of the non-autonomous equation, and we provide a non-autonomous M\"obius transformation to another equation found in [Hietarinta J., J. Nonlinear Math. Phys. 12 (2005), suppl. 2, 223-230] and appearing also in Boll's classification [Boll R., Ph.D. Thesis, Technische Universit\"at Berlin, 2012].
Keywords
Cite
@article{arxiv.1705.00298,
title = {Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation},
author = {Giorgio Gubbiotti and Christian Scimiterna},
journal= {arXiv preprint arXiv:1705.00298},
year = {2019}
}
Comments
In order that the manuscript be reasonably self contained, we have used some introductory material from our paper arXiv:1704.05805 to provide background for the presentation made here