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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2018 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209460 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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].
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| ISSN: | 1815-0659 |