Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation
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 arbitrar...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Sprache: | English |
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Інститут математики НАН України
2018
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| Zitieren: | Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation / G. Gubbiotti, C. Scimiterna // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 63 назв. — англ. |
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Gubbiotti, G. Scimiterna, C. 2025-11-21T19:14:55Z 2018 Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation / G. Gubbiotti, C. Scimiterna // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 63 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 37K35; 37L20; 37L60; 39A14; 39A22 arXiv: 1705.00298 https://nasplib.isofts.kiev.ua/handle/123456789/209460 https://doi.org/10.3842/SIGMA.2018.004 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 QV 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]. We would like to thank Professor Decio Levi for the many interesting and fruitful discussions during the preparation of this paper. We thank the anonymous referees for their suggestions on how to improve the paper. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation |
| spellingShingle |
Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation Gubbiotti, G. Scimiterna, C. |
| title_short |
Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation |
| title_full |
Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation |
| title_fullStr |
Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation |
| title_full_unstemmed |
Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation |
| title_sort |
reconstructing a lattice equation: a non-autonomous approach to the hietarinta equation |
| author |
Gubbiotti, G. Scimiterna, C. |
| author_facet |
Gubbiotti, G. Scimiterna, C. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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 QV 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].
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209460 |
| citation_txt |
Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation / G. Gubbiotti, C. Scimiterna // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 63 назв. — англ. |
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AT gubbiottig reconstructingalatticeequationanonautonomousapproachtothehietarintaequation AT scimiternac reconstructingalatticeequationanonautonomousapproachtothehietarintaequation |
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2025-11-25T23:48:54Z |
| last_indexed |
2025-11-25T23:48:54Z |
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1850885966987788288 |