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

Symmetry Integrability and Geometry-Methods and Applications

article

Nobutaka Nakazono¹ 

[1] Institute of Engineering, Tokyo University of Agriculture and Technology

关键词: lattice sine-Gordon equation;    Lax pair;    integrable systems;    partial difference equations.;   

DOI  :  10.3842/SIGMA.2022.032

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown