Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 100, 14 pages      arXiv:1106.0636      https://doi.org/10.3842/SIGMA.2011.100
Contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)”

Families of Integrable Equations

Pavlos Kassotakis a and Maciej Nieszporski b
a) Department of Mathematics and Statistics University of Cyprus, P.O. Box: 20537, 1678 Nicosia, Cyprus
b) Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski, ul. Hoza 74, 00-682 Warszawa, Poland

Received May 23, 2011, in final form October 20, 2011; Published online October 28, 2011

Abstract
We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through Bäcklund transformations. At least one of the members of each family is integrable, hence the whole family inherits some integrability properties.

Key words: integrable lattice equations; Yang-Baxter maps; consistency around the cube.

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