Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation

Symmetry Integrability and Geometry-Methods and Applications

article

Giorgio Gubbiotti¹  Christian Scimiterna² 

[1] School of Mathematics and Statistics, The University of Sydney;Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre and Sezione INFN di Roma Tre

关键词: quad-equations;    Darboux integrability;    algebraic entropy;    generalized symmetries;    exact solutions;   

DOI  :  10.3842/SIGMA.2018.004

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $Q_{\rm V}$ equation, and we provide a non-autonomous Möbius 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 Universität Berlin, 2012].

【 授权许可】

Unknown