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SIGMA, 2018, Volume 14, 004, 21 pages (Mi sigma1303)  

This article is cited in 1 scientific paper (total in 1 paper)

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

Giorgio Gubbiottiabc, Christian Scimiternaca

a Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre
b School of Mathematics and Statistics, F07, The University of Sydney, New South Wales 2006, Australia
c Sezione INFN di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy

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 $Q_V$ 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].

Keywords: quad-equations; Darboux integrability; algebraic entropy; generalized symmetries; exact solutions.

Funding Agency Grant Number
Instituto Nazionale di Fisica Nucleare IS-CSN4
Australian Research Council FL120100094
GG is supported by INFN IS-CSN4 Mathematical Methods of Nonlinear Physics and by the Australian Research Council through an Australian Laureate Fellowship grant FL120100094.


DOI: https://doi.org/10.3842/SIGMA.2018.004

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Bibliographic databases:

MSC: 37K10; 37K35; 37L20; 37L60; 39A14; 39A22
Received: April 30, 2017; in final form December 15, 2017; Published online January 9, 2018
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Citation: Giorgio Gubbiotti, Christian Scimiterna, “Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation”, SIGMA, 14 (2018), 004, 21 pp.

Citation in format AMSBIB
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\by Giorgio~Gubbiotti, Christian~Scimiterna
\paper Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation
\jour SIGMA
\yr 2018
\vol 14
\papernumber 004
\totalpages 21
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\crossref{https://doi.org/10.3842/SIGMA.2018.004}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Giorgio Gubbiotti, Christian Scimiterna, Ravil I. Yamilov, “Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions”, SIGMA, 14 (2018), 008, 51 pp.  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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