This article is cited in 13 papers

Families of Integrable Equations

Pavlos Kassotakis^a, Maciej Nieszporski<sup>b

a</sup> 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

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.

Keywords: integrable lattice equations, Yang–Baxter maps, consistency around the cube.

MSC: 82B20; 37K35; 39A05

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

Language: English

DOI: 10.3842/SIGMA.2011.100

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ArXiv: 1106.0636