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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 032, 8 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.032 (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
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DOI: https://doi.org/10.3842/SIGMA.2022.032
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.
Funding agency Grant number
Japan Society for the Promotion of Science JP19K14559
This research was supported by a JSPS KAKENHI Grant Number JP19K14559.
Received: February 3, 2022; in final form April 14, 2022; Published online April 20, 2022
Bibliographic databases:
Document Type: Article
MSC: 37K10, 39A14, 39A45
Language: English
Citation: Nobutaka Nakazono, “Properties of the Non-Autonomous Lattice Sine-Gordon Equation: Consistency around a Broken Cube Property”, SIGMA, 18 (2022), 032, 8 pp.
Citation in format AMSBIB
\Bibitem{Nak22}
\by Nobutaka~Nakazono
\paper Properties of the Non-Autonomous Lattice Sine-Gordon Equation: Consistency around a Broken Cube Property
\jour SIGMA
\yr 2022
\vol 18
\papernumber 032
\totalpages 8
\mathnet{http://mi.mathnet.ru/sigma1826}
\crossref{https://doi.org/10.3842/SIGMA.2022.032}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4409887}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129231379}
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