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

@article{Nakazono2022PropertiesOT, title={Properties of the Non-Autonomous Lattice Sine-Gordon Equation: Consistency around a Broken Cube Property}, author={Nobutaka Nakazono}, journal={Symmetry, Integrability and Geometry: Methods and Applications}, year={2022} }

A bstract . The lattice sine-Gordon equation is an integrable partial di ﬀ erence equation on 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.

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