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

SIGMA 18 (2022), 032, 8 pages      arXiv:2201.11264      https://doi.org/10.3842/SIGMA.2022.032

Properties of the Non-Autonomous Lattice Sine-Gordon Equation: Consistency around a Broken Cube Property

Nobutaka Nakazono
Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho Koganei, Tokyo 184-8588, Japan

Received February 03, 2022, in final form April 14, 2022; Published online April 20, 2022

Abstract
The lattice sine-Gordon equation is an integrable partial difference equation on ${\mathbb Z}^2$, which approaches the sine-Gordon equation in a continuum limit. In this paper, we show that the non-autonomous lattice sine-Gordon equation has the consistency around a broken cube property as well as its autonomous version. Moreover, we construct two new Lax pairs of the non-autonomous case by using the consistency property.

Key words: lattice sine-Gordon equation; Lax pair; integrable systems; partial difference equations.

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