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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2018
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| Online Zugang: | 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 |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |