We study the discrete Darboux transformation and construct multi-soliton solutions in terms of the ratio of determinants for the integrable discrete sine-Gordon equation. We also calculate explicit expressions of single-, double-, triple-, and quadruple-soliton solutions as well as single- and double-breather solutions of the discrete sine-Gordon equation. The dynamical features of discrete kinks and breathers are also illustrated.

中文翻译：

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离散正弦-Gordon方程的Darboux变换和多孤子解

我们研究离散Darboux变换，并根据可积离散正弦Gordon方程行列式的比率构造多孤子解。我们还计算了单，双，三和四孤子解决方案以及离散正弦-Gordon方程的单和双喘息解决方案的显式表达式。还显示了离散的扭结和通气的动态特征。