Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions
In this paper, we construct the general solutions of two families of quad-equations, namely the trapezoidal H⁴ equations and the H⁶ equations. These solutions are obtained exploiting the properties of the first integrals in the Darboux sense, which were derived in [Gubbiotti G., Yamilov R.I., J. Phy...
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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/123456789/209456 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions / G. Gubbiotti, C. Scimiterna, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 46 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731349063892992 |
|---|---|
| author | Gubbiotti, G. Scimiterna, C. Yamilov, R.I. |
| author_facet | Gubbiotti, G. Scimiterna, C. Yamilov, R.I. |
| citation_txt | Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions / G. Gubbiotti, C. Scimiterna, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 46 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we construct the general solutions of two families of quad-equations, namely the trapezoidal H⁴ equations and the H⁶ equations. These solutions are obtained exploiting the properties of the first integrals in the Darboux sense, which were derived in [Gubbiotti G., Yamilov R.I., J. Phys. A: Math. Theor. 50 (2017), 345205, 26 pages]. These first integrals are used to reduce the problem to the solution of some linear or linearizable non-autonomous ordinary difference equations, which can be formally solved.
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| first_indexed | 2025-12-07T19:25:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209456 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:25:10Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gubbiotti, G. Scimiterna, C. Yamilov, R.I. 2025-11-21T19:12:12Z 2018 Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions / G. Gubbiotti, C. Scimiterna, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 46 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 37L60; 39A14 arXiv: 1704.05805 https://nasplib.isofts.kiev.ua/handle/123456789/209456 https://doi.org/10.3842/SIGMA.2018.008 In this paper, we construct the general solutions of two families of quad-equations, namely the trapezoidal H⁴ equations and the H⁶ equations. These solutions are obtained exploiting the properties of the first integrals in the Darboux sense, which were derived in [Gubbiotti G., Yamilov R.I., J. Phys. A: Math. Theor. 50 (2017), 345205, 26 pages]. These first integrals are used to reduce the problem to the solution of some linear or linearizable non-autonomous ordinary difference equations, which can be formally solved. We would like to thank Professor Decio Levi for the many interesting and fruitful discussions during the preparation of this paper. We are also grateful to the anonymous referees whose comments greatly helped us in improving the paper. GG has been 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 Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions Article published earlier |
| spellingShingle | Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions Gubbiotti, G. Scimiterna, C. Yamilov, R.I. |
| title | Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions |
| title_full | Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions |
| title_fullStr | Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions |
| title_full_unstemmed | Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions |
| title_short | Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions |
| title_sort | darboux integrability of trapezoidal h⁴ and h⁶ families of lattice equations ii: general solutions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209456 |
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