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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2022 Volume 18, 032, 8 pp. (Mi sigma1826)

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

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.

Keywords: lattice sine-Gordon equation, Lax pair, integrable systems, partial difference equations.

MSC: 37K10, 39A14, 39A45

Received: February 3, 2022; in final form April 14, 2022; Published online April 20, 2022

Language: English

DOI: 10.3842/SIGMA.2022.032



Bibliographic databases:
ArXiv: 2201.11264


© Steklov Math. Inst. of RAS, 2026