The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and the method of additional independent variables. Then the symmetric reduction of discrete Darboux equations with sources is presented. In order to provide a simpler version of the resulting equations we introduce the τ/σ form of the (commutative) discrete Darboux system. Our equations give, in continuous limit, the version with self-consistent sources of the classical symmetric Darboux system.

中文翻译：

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具有自洽源的离散Darboux系统及其对称约简

利用矢量基本（二进制Darboux）变换和附加自变量方法，构造了具有自洽源的离散非交换Darboux方程组。然后给出了带有源的离散达布克斯方程的对称约简。为了提供所得方程的更简单形式，我们介绍了（可交换）离散Darboux系统的τ / σ形式。我们的方程式在连续的极限中给出了具有经典对称Darboux系统的自洽源的版本。