Darboux Integrability of Trapezoidal H⁴ and H⁶ Families of Lattice Equations II: General Solutions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Gubbiotti, G., Scimiterna, C., Yamilov, R.I.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209456
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...